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Question

A positive number is divided into two parts such that the sum of the squares of the two parts is 20. the square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

Solution
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x is the smaller part. Let y be the bigger part.
y2+x2=20
y2=8x [so, x>0 …………(1)]
x2+8x=20
x=2;x=10
So, x=2 (from (1))
y2=8x=16
y=4 [x+y is positive]
So, number=x+y=2+4=6.

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