Question

Divide 12 into two parts such that the sum of their squares is 74.

Answer 1

Let the first number be ‘X’, so the other number will be ’(12–X)’.

∵ X² + (12 – X)² = 74

X² + 144 + X² – 24X = 74

On simplifying further,

2X² – 24X + 70 = 0

X² – 12X + 35 = 0

On applying Sreedhracharya formula

∴ X = 5 or X = 7.

Then other numbers will be (12–X) = {12–5} & {12–7} i.e., 7 or 5.

∴ The number 12 is divided into two parts namely 5 & 7.