Question

the difference of the squares of 2 numbers is 180. the square of the smaller number is 8 times the larger number. find the 2 numbers.

Answer 1

Answer:

Let the larger number = x

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

and the square of the larger numbe r = x

According to the question,

x - 8x = 180

=> x - 8x - 180 = 0

=> x - 18x + 10x - 180 = 0

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

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

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

=> x = 18 or x = -10

Thus, the larger number = 18 or -10

Then, the square of the smaller number = 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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