Question 78

In the following question, state whether the statement is True (T) or False (F):

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

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Solution

True
We have, $51^{2} - 49^{2} = 100 p$
$\Rightarrow (51 + 49) (51 - 49) = 100 p$ $[∵ a^{2} - b^{2} = (a + b) (a - b)]$
$\Rightarrow 100 \times 2 = 100 p$
$\Rightarrow p = 2$

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