# The difference of squares of two numbers is 400. The square of the smaller number is 9 times the larger number. Find the two numbers. â€‹

We are given that the difference of squares of  two numbers is 400. The square of the smaller number  is 9 times the larger number.

Let the larger number be   and smaller number be .

First condition states that the difference of squares of  two numbers is 400, that means;

----------- [Equation 1]

Second condition states that the square of the smaller number  is 9 times the larger number, that means;

Putting this in equation 1, we get;

Now, we will use middle term splitting method;

.

Hence,   x= 25 . Since, x = -16 is not possible to take so the larger number .

Now, putting value of x in equation 1 we get;

= 625 - 400 = 225

Therefore, the smaller number is y = 15.

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