Germany | Can you solve this ? | Olympiad Mathematics

[00:00:00]Hello. You're welcome to solve this math problem of square root of a over 2a is equal to 10.

[00:00:09]To find the value of a from this equation.

[00:00:13]Now, from here, which is square root of a over 2a, to remove the square root, we square on both sides. So, here it will be bracket square is equal to Also, here it will be 10 square.

[00:00:31]Then, in the next step, here we take square in the numerator and in the denominator. So, it will be square root of a bracket square over Also, in the denominator, it will be 2a bracket square is equal to 10 square, it is 100.

[00:00:52]Then, into here, this square root will cancel square. So, it will be a over Here, we take square inside, so it will be 2 square, it is 4 * a square is equal to 100.

[00:01:09]Then, here is same as 100 over 1. So, into here, we will cross multiply. So, it will be a * 1, it is a is equal to 4a square * 100, it is 400 a square.

[00:01:27]Then, into here, we take a to this side.

[00:01:29]So, it will be this, which is 400 a square. We take a to this side, so it will be minus a is equal to zero.

[00:01:40]Then, into here, a it is common. So, we [clears throat] take a outside the bracket. 400 a square divided by a, it is 400 a.

[00:01:50]Then, minus a divided by a, it is minus 1 bracket is equal to zero.

[00:01:58]Then, from here we have two solutions where this first solution of A is equal to zero and this second solution of 400 A minus one is equal to zero.

[00:02:13]Then here we've got A is equal to zero.

[00:02:15]Here we take negative one to this side so it will be 400 A negative one we take this side it will be is equal to one.

[00:02:25]Then we divide by 400 in both sides.

[00:02:29]Also into this side we divide by 400. So this and this will cancel then it will be A is equal to one over 400.

[00:02:42]Now here we've got A is equal to zero and here A is equal to one over 400.

[00:02:49]In the next step we will check for these solutions.

[00:02:52]Now let's solve by using another method.

[00:02:58]So from our problem which is this here which is square root of A over 2 A is equal to 10.

[00:03:10]To find the value of A.

[00:03:12]Now into here this is same as 10 over one.

[00:03:16]So here we will cross multiply. So it will be A square root of A times one it is square root of A is equal to 2 A times 10. So here 2 A times 10.

[00:03:31]Then here it will be square root of A is equal to 2 A times 10 is 20 A.

[00:03:40]Then into here we will to remove the square root we square on both sides. So here it will be square root of A bracket square is equal to 20 a bracket square.

[00:03:57]So here this square root will cancel square. So it will be a is equal to 20 square.

[00:04:06]times a square Then here it will be a is equal to 20 square. It is 400 times a square.

[00:04:18]Then we take a to this side. So it will be 400 a square. A take this side will be minus a is equal to zero.

[00:04:29]Then into here a is common. So we take a outside the bracket. 400 a square divided by a it is 400 a.

[00:04:39]minus a divided by a it is minus one bracket is equal to zero.

[00:04:45]Then from here we have two solutions of a is equal to zero and this solution here of 400 a minus one is equal to zero.

[00:04:59]Then here we got a is equal to zero.

[00:05:01]Here we take negative one to this side.

[00:05:03]So it will be 400 a is equal to one.

[00:05:09]Then here we divide by 400 both sides.

[00:05:11]So here over 400 and here over 400. So this and this will cancel. Then it will be a is equal to one over 400.

[00:05:25]Now in the next step let's check this our answers if they are correct.

[00:05:30]So to check from our problem which is square root of a over 2 a is equal to 10.

[00:05:41]Here we substitute a is equal to zero.

[00:05:43]So here it will be square root of a is zero. So, square root of zero over two times A is zero. Is it equal to this 10?

[00:05:56]Now, from square root of zero, it is zero over two times zero is zero. Then, is it equal to 10?

[00:06:06]Now, zero divided by zero is undefined.

[00:06:13]This undefined is not equal to 10.

[00:06:17]So, here A is not is equal to zero, this is not the correct. So, this solution is rejected.

[00:06:26]Same as into the here our solution, this here is not correct.

[00:06:31]Now, let's check for A is equal to 1 over 400. Same as here, A is equal to 1 over 400.

[00:06:40]>> [snorts] >> Now, into here into our problem, whereas our problem is square root of A over 2 A is equal to 10.

[00:06:53]Now, into here square root of A, so here it will be square root of A, our A we substitute our answer 1 over 400.

[00:07:05]Then, over two times A, our A we substitute this our answer 1 over 400. Then, is it equal to this 10?

[00:07:21]Then, from here square root of 1 over 400. So, here it will be square root of 1, we separate, so it will be square root of 1 over square root of 400.

[00:07:37]Then, over here it will be two times one is 2. 2 over 400. So, here 2 over 400. Then, is it equal to 10?

[00:07:53]Then, into here square root of 1 it is 1 over square root of 400 it is 20.

[00:08:06]Then, over this here 2 over 400. So, 2 over 400. Is it equal to 10?

[00:08:18]Then, here it will be 1 over 20 * here divided by 2 over 400 is same as reciprocal * 400 over 2. Is it equal to 10?

[00:08:34]Now, here to simplify this zero cancels this zero. Then, this two it will be 20.

[00:08:42]Then, 1 * 20 is 20. 20 / 2 is 10 is equal to 10.

[00:08:48]So, left side and right side are equal.

[00:08:51]Then, it is true for the value of A is this 1 over 400.

[00:08:56]Same as also into this solution here A is 1 over 400.

[00:09:05]So, this is the only value of A.

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[00:09:17]Bye-bye.