The solution of $(x + 2)^{2} - (x - 3)^{2} = 15$ is

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Solution

The correct option is C 2
${(x + 2)}^{2} - {(x - 3)}^{2} = 15$
Using identity:
${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$
Therefore,
${(x + 2)}^{2} - {(x - 3)}^{2} = 15$
$(x^{2} + 4 + 4 x) - (x^{2} + 9 - 6 x) = 15$
$\Rightarrow x^{2} + 4 + 4 x - x^{2} - 9 + 6 x = 15$
$\Rightarrow 10 x - 5 = 15$
$\Rightarrow 10 x = 15 + 5$
$\Rightarrow x = \frac{20}{10} = 2$
Hence the correct answer is $2$ .

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