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.(solve by completing the square method)

Answer 1

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 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 number are 12 and and 18

Hope this helps you friend
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