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Question

the difference of the square of two number is 180 the square of the smaller number is 8 times the larger number find the two numbers


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 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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