00:02
Hello, the ratio of two numbers, let the numbers be x and y, is given to be 1 is to 2 and it's given that the sum of their squares, that is x square plus y square is equal to 20.
00:22
We have to find all possible pairs of numbers x y, we satisfy these conditions.
00:29
So, when two numbers are in this ratio, the general form is x equal to 2 times some constant and y is equal to 2 times some, the same constant.
00:42
Then let us plug in x equal to 2k and y equal to 2k, sorry, the, if two numbers are in the ratio 1 is to 2, the general form is x equal to 1 times k and y equal to 2 times k for some common constant k.
01:02
Now let us take x equal to 1k, x equal to k and y equal to 2k and plug into this condition, we get k square plus y equal to 2k, so square of it is 4k square equal to 20.
01:20
This implies 5k square equal to 20.
01:25
This implies k square, if we divide by 5, both sides of this equation, we get k square equal to 4...