# 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.

18, 12; - 18, - 12

Let the larger number be x and smaller number be y

x2 – y2 = 180 …Equation (i)

Since the square of the smaller number is 8 times the larger number, so

x2 – 8x - 180 = 0

Performing factorization we get:

x2 - 18x + 10x - 180 = 0

x(x - 18) + 10(x - 18) = 0

(x + 10)(x - 18) = 0

x = - 10,18

Rearranging Equation (i)

y2 = x2 - 180

Putting x = - 10 we get

y2 = - 80

Since the square is negative so the solution is neglected

Putting x = 18 we get

y2 = 144

y = 12

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