Q78 of 128 Page 224

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

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

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.


Hence, the statement is true.


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