Question

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

Answer 1

Answer:

The two parts are 13 and 16

Step-by-step explanation:

Let the two parts be "x" and "29 - x"

The sum of squares of these two parts is 425

Hence,

x² + (29 - x)² = 425

x² + 841 - 58x + x² = 425

2x² - 58x + 416 = 0

x² - 29x + 208 = 0

x² - 13x - 16x + 208 = 0

x(x - 13)  -16(x - 13) = 0

(x - 16)(x - 13) = 0

x = 16 or x = 13

If x = 16 then 29-x = 13

If x = 13 then 29-x = 16

Whichever way we look at it, the two required parts of 29 are 13 and 16.