Question

A positive number is divided into two parts such that the sum of the squares of the two parts is 208. The square of the larger part is 18 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 = 18x

Sum of the squares of the two parts is 208.

x² + y² = 208

x² + 18x - 208 = 0

x² + 26x - 8x + 208 = 0

x(x + 26) - 8(x + 26) = 0

(x - 8)(x + 26) = 0

x = 8 or x = -26 (rejected as part of pice never be negative)

y = √18x

=√18 x 8

= √144

= 12

Hence, the no. is 8 + 12 = 20