The value of p for 51^2 – 49^2 = 100 p is 2.

Question

State whether the statements are true (T) or false (F)

The value of p for 51² – 49² = 100 p is 2.

Answer 1

True

Solving for p,

(51)² – (49)² = 100p

⇒ (50 + 1)² – (50 – 1)² = 100p [∵, 51 = 50 + 1 & 49 = 50 – 1]

⇒ (2500 + 1 + 100) – (2500 + 1 – 100) = 100p [∵, (a + b)² = a² + b² + 2ab and (a – b)² = a² + b² – 2ab)]

⇒ 2500 + 1 + 100 – 2500 – 1 + 100 = 100p

⇒ 200 = 100p

⇒ 100p = 200

⇒ p = 200/100 = 2

The value of p is 2.