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.

Answer 1

Let the smaller and larger of two parts be x and y.

According to question

y2 = 8x

Sum of the squares of the two parts is 20.

x2 + y2 = 20

x2 + 8x - 20 = 0

x2 - 2x + 10x - 20 = 0

x(x - 2) + 10(x - 2) = 0

(x - 2)(x + 10) = 0

x = 2 or x = -10 (rejected as part of pice never be negative)

y2 = 8x

y = √8x

=√8 x 2

= √16

= 4

Hence, the no. is 2 + 4 = 6