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.
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.