Question

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

Answer 1

Let one part be x

then another part will be (29 - x)

Now, ATQ

x^2 + (29 - x)^2 = 425

x^2 + 841 + x^2 - 58x = 425

2x^2 - 58x + 841 - 425 = 0

2x^2 - 58x + 416 = 0

2x^2 - 32x - 26x + 416 = 0

2x(x-16) - 26 (x-16) = 0

(2x-26) (x-16) = 0

x = 26/2, 16 = 13, 16

two numbers are 13 and 16