Question

Divide 29 into two parts so that the sum of squares of the parts is 425.​

Answer 1

Let the parts be x and 29 – x

According to the problem

x² + (29 – x)² = 425

⇒ x² + 841 + x² – 58x – 425 = 0

⇒ 2x² - 58x + 416 = 0

⇒ x² – 29x + 208 = 0

⇒ x² – 16x – 13x + 208 = 0

⇒ x(x - 16) – 13(x – 16) = 0

⇒ (x - 16)(x – 13) = 0

⇒ x – 16 = 0 or x – 13 = 0

⇒ x = 16 or x = 13

When x = 16, then 29 - x = 13

When x = 13, then 29 - x = 16

Hence, the parts are 13 and 16.