Question

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 1

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-: Solution:-

Let the larger number = x Then the square of the smaller number = 8 times the larger number = 8x

and the square of the larger number = x According to the question, => x- 8x 180 = 0 Thus, the larger number = 18 or -10 Then, the square of the smaller number =

x - 8x = 180

=> x 18x + 10x - 1800

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

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

=> x = 18 or x = -10

8(18) or 8(-10)

= 144 or -80

The square of a number can't be negative,

so, the square of smaller number = 144 Hence, the smaller number = sqrt(144) = 12

The numbers are 12 and 18

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Final Answer:-

The numbers are 12 and 18

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