(Q25)The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Answer

Let the large number be x.

8 times larger number = Square of the smaller number = 8x

Square of the larger number = x2

By problem, x2-8x=180

x2 - 8x - 180 = 0

x2 - x + 10x - 180 = 0

x(x - ) + 10(x-) = 0

(x + 10)(x - ) = 0

x + 10 = 0 or x - = 0

x = -10 or x =

If x = , the larger number = ;

(smaller number)2 = 8 × =

∴ Small number = √ =

The numbers are ,

Note: Discard x = -10.