Is the following equation a quadratic equation?
$(x + 2)^{3} = x^{3} - 4$

Yes

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Ambiguous

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Data insufficient

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Solution

The correct option is A Yes
Given equation is $(x + 2)^{3} = x^{3} - 4$
$\to x^{3} + 2^{3} + 3 \times x \times 2 (x + 2) = x^{3} - 4$
$\Rightarrow x^{3} + 8 + 6 x (x + 2) = x^{3} - 4$
$\Rightarrow x^{3} + 8 + 6 x^{2} + 12 x - x^{3} + 4 = 0$
$\Rightarrow 6 x^{2} + 12 x + 12 = 0$
Comparing it with the standard form of quadratic equation $x^{2} + b x + c = 0, a \neq 0$ .
Here, $a = 6$
Thus, it is a quadratic equation.

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