Question

if p+q =r and p-q =s prove that r2+s2=2(p2+q2).

Answer 1

hope this helps you ☺

Answer 2

Given:

p + q = r and p - q = s

To Prove:

r² + s²=2(p²+q²)

Solution:

As given,

p + q = r ------ (1)

p - q = s------- (2)

now squaring and adding both equation,

⇒ (p + q)² + (p - q)² = r² + s²

⇒ p² + q² + 2pq + p² + q² - 2pq =  r² + s²

⇒  p² + q² + p² + q² =  r² + s²

⇒ 2p² + 2q² = r² + s²

⇒ 2( p² + q²) =  r² + s²

Hence, proved.