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Differences of Squares of Triangular Numbers and Converse

If 2p + 2 +...

Question

If $2^{p + 2} + 2^{p + 1} = 96$ , then find the value of $p$ .

A

1

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B

2

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C

3

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D

4

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E

5

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Solution

The correct option is D $4$
As given, $2^{p + 2} + 2^{p + 1} = 96$
Rewriting the left hand side of equation using $x^{a} . x^{b} = x^{a + b}$ .
$2^{p} {.2}^{2} + 2^{p} {.2}^{1} = 96$
$2^{p} (2^{2} + 2^{1}) = 96$
$2^{p} \times 6 = 96$
$2^{p} = 16 = 2^{4}$
$p = 4$
Hence, option D is correct.

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Differences of Squares of Triangular Numbers and Converse

Standard VIII Mathematics

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