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.