Question

Separate 18 into 2 parts such that twice the sum of their squares is five times their product.

Answer 1

Let the two parts of 18 be x and 18 − x.

According to the given condition:

Twice the sum of their squares is five times their product.

2[x² + (18 − x)²] = 5 [x(18 − x)]

2[x² + 324 − 36x + x²] = 5(18x − x²)

2(2x² − 36x + 324) = 90x − 5x²

4x² − 72x + 648 = 90x − 5x²

9x² − 162x + 648 = 0

Divide throughout by 9:

x² − 18x + 72 = 0

(x − 6) (x − 12) = 0

x = 6 or x = 12