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Showing posts with label equations. Show all posts
Showing posts with label equations. Show all posts

4.09.2016

The equation a fraction

What if the equation of lead shot, and X is hidden in the denominator? We need to get rid of the denominator. What will happen with X? Do not worry. If you do everything correctly, he from the denominator goes into the numerator. Here you can recommend two ways to solve the equation.

The first method is to bring the expression to normal proportions. Then we use the proportion of the property - the multiplication of extreme terms in proportion equal to the multiplication of the average proportion of members. Denominator magically disappear. We get a simple equation, which can be easily solved. Consider an example.

The equation a fraction. Mathematics For Blondes.
The equation a fraction

The number did not work nicely. Make checks and look at the result. Substitute the original expression instead of X its value.


Checking equation. The equation a fraction. Mathematics For Blondes.
Checking equation

The audit showed that the equation is solved correctly.

The second method is to bring the expression to a common denominator. The denominator should be common to the left and right sides of the equation. In this case, we in good conscience can throw the denominator in the trash. We see an example of reduction to a common denominator.

The equation a fraction. Method is to bring the expression to a common denominator. Mathematics For Blondes.
The equation a fraction
The result was the same as in the first case.

8.26.2012

Unsolvable equalizations are in preschool

The decision of unsolvable equalization caused some questions. Now we on the other hand will look at unsolvable equalization a number 1:

x + 2 = x

For this purpose we will create task research force and will nose after her behavior. In a research group we will plug:

1) Child from preschool. He only begins to understand the elements of mathematics but already considers well.
2) Blonde, mother of child from preschool. Once at school taught mathematics and knew it well. Now she forgot everything.
3) Professor of mathematics De Colletage. Brilliantly owns a mathematical vehicle, decides the most intricate mathematical problems.
4) Nikolay Khyzhnjak. Engineer, addicts to mathematics, asserts that understands this abstract science.

You will say that it is not honest, to include itself in the complement of research group. But, respected, I thought of this group, I offered candidates in her composition, I assert final composition of research group. It is the most democratic principle. I honestly took advantage of democratic right to be select and won in the competition of candidates :)))

And so, we will ask our research group to decide a simple task and give the algebraic variant of her decision:

We have an unknown amount of hedgehogs to that added two grass-snakes. How many hedgehogs did turn out?

As a result a research group gave out next decisions.

1) Child from preschool. As I talked already, a child is clever and able to decide logical tasks, in that it is needed to guess the train of thoughts of author of task and give the same answer that waits from a child author of task. It is such method of training of future zombis, that is well able to guess that is waited from them by owners. A child answered the unknown amount of hedgehogs" will "Turn out. On a request to write down the decision of this task on the sheet of paper, a child answered that to write he is not yet able, but can draw a hedgehog.

2) Blonde, mother of child from preschool. A blonde correctly decided a task after the row of leading questions. On a request to write down the decision through algebra, she began to reason: "Algebra, algebra... Nothing I remember... Algebra means - this unknown... Wow! We will designate the unknown amount of hedgehogs through "х". The amount of grass-snakes is known us and designating him is not needed, simply a number we write... Addition for us - it a sign "plus". Here"!. A blonde stretches out the sheet of paper, it is writtenin on that:

x + 2 = x

3) Professor of mathematics De Colletage. On a request to decide a task about hedgehogs and grass-snakes a famous professor was indignant, that it is ashamed to the great scientist to decide such child's tasks. He sent us after the decision of task in kindergarten. On our request to write down the algebraic decision of this task, a professor непонимающе looked at us, long thought and said: "Well, I will think above this problem". And was farther following...

For the algebraic reflection of decision of this task a professor worked out the special theory of three-cornered integrals, for that him was awarded with rank "academician". To the three-cornered integral the name of author was appropriated and he began to be named "Three-cornered integral De Colletage"...

For the decision of this concrete task the special research institute was created at the head with now already by an academician De Colletage. After a few years of the strained work, multivolume scientific work bore under the name "Practical application of three-cornered integral De Colletage in limits on the radius of cut on a dress"...

All of it nearscientific delirium we we will not study. We are interested only by a result. At once we open the last page of the last volume. There list of some organizations... We leaf pages to beginning of book in search of answer for a task... Somewhere in the middle of the last volume we find a line "Hired executed on account of working off scientific underbacks : .". Oho! This gang of easy riders from science on an even place managed to guzzle the whole lot of moneys! And before this line it is possible to find an answer for our task. "Х" is there written with plenty of reservations.

4) Nikolay Khyzhnjak. This witch-doctor of mathematics profoundly gave out a page under the name "Decision of unsolvable equalizations". According to his opinion, there is other task in that asked, how many hedgehogs will turn out, if to two hedgehogs to add the unknown amount of grass-snakes. He assures that both tasks have an identical decision :)))

By the way, there is another interesting task about grass-snakes and hedgehogs:

Mixture of grass-snake and hedgehog is a meter of the barbed wire. How mathematically to write down this expression?

Unsolvable equalizations are in preschool. Mixture of grass-snake and hedgehog is a meter of the barbed wire. Mathematics for blondes.
Three-cornered integral De Colletage on the cut of dress not to apply :)))

8.15.2012

Decision of unsolvable equations

In comments to the article infant "Wunderkindes and cretin with blondes" (in Russian language) me offered to decide a few equations it is "known from a digit, that a decision is not present". These equations look like the following:

1) x + 2 = x

2) √x = -1

3) x/0 = x


Probably, on mathematicians these unsolvable equations operate, as a boa on rabbit and infuse with in their souls the awesome trembling. I am deprived such superstitions. Moreover, the author of this idea, Vag, tossed up to me a magic stick:

"Decisions does not have" means that it is WELL-PROVEN that such circumstances at that problem abode by ARE not.

Today we will consider circumstances at that terms at least one of equations observed. Consequently, at least one unsolvable equation we will decide now.

But to begin would I like not from a decision, and from an answer to the question: "Where these unsolvable equations appeared from?" Me it seems to, here from where...

...A mother bought to the child a new toy are blocks with an alphabet. She collected a few words from blocks, read them and gave blocks to the child. A mother took up the everyday businesses.

Blocks with an alphabet. Mathematics for blondes.
A child with enthusiasm began to fold blocks. Finishing to lay out series from the blocks taken by chance, he put question to the mother:

- That is here written?

- Nothing. You laid down letters wrong, - a mother explained, - When will learn letters, then you will be able correctly to fold blocks.

A child was very offended and burst into tears. What a more mother tried to quiet him, the he cried stronger. Then a mother said:

- Well, try once again, I necessarily will read you.

Bustling a nose, a child at random took a few blocks and laid down them in series.

- What did I write? - he asked with tears.

Farther not to disorder a child, a mother answered:

- In mathematics a certain integral is so designated in limits from Old Testament to nine evening, taken on the surface of asynchronous point.

A child quieted down puzzled. He understood nothing, but something disturbed him in this phrase. A bit thinking, he asked:

- And will a fairy-tale be at nine o'clock of evening?

- It will be necessarily. Where will she go? - a mother answered very confidently.

Very attentively looking to the mother in eyes, a child by touch took a few blocks and laid down another abracadabra.

- And it what did I write? - he asked with distrust, not tearing away a look from mother eyes.

If a mother will not look at blocks will say that is written there, she means cheats him. If will look - she means that is written there really reads.

A mother looked another portion of incoherent words at blocks and crfpfkf. A child was happy. He has the most clever mother! Farther this game proceeded until child not tired of. He really had a clever mother that knew many clever words.

A child grew up then, learned letters, began independently to fold words from blocks. When he became adult, he forgot playing blocks, but faith that for him the most clever mother, remained...

Just as a child made blocks, mathematicians worked out unsolvable equations from mathematical symbols. A child grew and became adult, mathematicians so remained in pampers of the determinations.

Now we will pass to business.

Decision of the first unsolvable equation

x + 2 = x


This equation traditionally can be taken to next equality

2 = 0

As this equality did not look wildly, but in mathematics such quite possible. I will say anymore, the first equation is only one equation from the system of two equations, that has one common decision. The second equation looks so:

2 + х = 2

This equation is usually taken to equality

х = 0

The decision of this system of equations looks so:

х ⊥ 2

It means that the numbers taken by you are on perpendicular numerical axes, therefore the rules of ordinary arithmetic give such result.

Decision of unsolvable equations. Mathematics for blondes.
I especially want to underline that all the known rule "from transposition of elements a sum does not change" in this case stops to work. A result depends on that, what number you take for basis at implementation of action of addition.

The further decision of this system of equalizations is possible two methods resulting in different results.

First method. Turn of one of numerical axes on 90 degrees and passing to the rules of ordinary addition. Undeniable equality will ensue:

x + 2 = x + 2

n this case the laws of symmetry of mathematical actions begin to work.

Second method. Remaining in the rectangular system of coordinates, to apply the methods of vectorial algebra and find a sum on the theorem of Pythagoras, where х and 2 are the cathetuses of rectangular triangle, and result of addition - by a hypotenuse. If you consider that application of facilities of vectorial algebra is impossible, when on the ends of sticks the tips of pointers are absent, then it is your personal problems already. In this case both equalizations of the system are taken to the identical decision:

x + 2 = √(x² + 2²)

It is done away with the decision of this unsolvable equalization. you need to be only determined with the desires - what result needs you.

Decision of the second unsolvable equalization.

√x = -1


This decision caused most difficulties from the simplicity. We erect both parts of equalization in a square and get an answer:

x = 1

This equalization is taken to equality:

+1 = -1

In the parallel instances of mathematics usually begin to dissert upon the modules of numbers. I will say that before to put signs before numbers, it is needed to understand sense of positive and negative numbers.

Decision of the third unsolvable equalization

x/0 = x


The decision of this equalization is taken to equality:

1 = 0

Personally for me there is nothing unusual in this equality. This one of basic equalities of mathematics, without that mathematics in principle is impossible. If our mathematicians until now do without this equality, then only due to the pampers. At exposition of mathematics on the pages of this web-site I will repeatedly call to this equality.

To accept the solutions offered by me or not accept is this your personal file. Monkeys too nobody compelled to go down on earth. Many of them until now on branches bruise along and fully happy without pampers))))