Question

If p,q are two consecutive odd numbers and p+q,pq,X are Pythagorean triple then find the value of x is. a)pq+2
b)p^2+q^2
c)(p+q)^2
d) 2pq

Answer 1

answer : option (A) 2 + pq

p and q are two consecutive odd numbers it means q - p = 2 , if we assume p < q.

now (p + q), pq and x are Pythagoras triple

from Pythagoras theorem,

h² = a² + b²

⇒ (p + q)² + (pq)² = x²

⇒p² + q² + 2pq + p²q² = x²

⇒(p - q)² + 2pq + 2pq + p²q² = x²

⇒ 4 + 4pq + p²q² = x²

⇒2² + 2.2.pq + (pq)² = x²

⇒(2 + pq)² = x²

⇒x = 2 + pq

hence, option (A) is correct choice.

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