Q. 74.2( 18 Votes )

# 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 :

18, 12; - 18, - 12

Let the larger number be x and smaller number be y

x^{2} – y^{2} = 180 …Equation (i)

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

⇒ x^{2} – 8x - 180 = 0

Performing factorization we get:

⇒ x^{2} - 18x + 10x - 180 = 0

⇒ x(x - 18) + 10(x - 18) = 0

⇒ (x + 10)(x - 18) = 0

x = - 10,18

Rearranging Equation (i)

y^{2} = x^{2} - 180

Putting x = - 10 we get

y^{2} = - 80

Since the square is negative so the solution is neglected

Putting x = 18 we get

y^{2} = 144

⇒ y = 12

Answer: 18,12 ;18, - 12

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