Question

Divide 29 into two parts so that the sum of the square 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             When x = 13
Then 29 - x = 13        Then 29 - x = 16
Hence, the parts are 16 and 13.