Q. 785.0( 1 Vote )

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

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

Answer :

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} = a^{2} + b^{2} + 2ab and (a – b)^{2} = a^{2} + b^{2} – 2ab)

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

⇒ 200 = 100p

⇒ 100p = 200

⇒ p = 200/100 = 2

The value of p is 2.

Hence, the statement is **true**.

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