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Question
The value of p for 512 – 492 = 100p is 2.
Options
True
False
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Solution
This statement is True.
Explanation:
Solving for p,
(51)2 – (49)2 = 100p
⇒ (50 + 1)2 – (50 – 1)2 = 100p ...[∵ 51 = 50 + 1 and 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.
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