Q7 of 58 Page 118

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


Answer: 18,12 ;18, - 12


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