Check whether the following are quadratic equation:
$x^{2} + 2 x + 1 = (4 - x)^{2} + 3$

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Solution

Given that, $x^{2} + 2 x + 1 = (4 - x)^{2} + 3$
$\Rightarrow x^{2} + 2 x + 1 = 16 + x^{2} - 8 x + 3$
$\Rightarrow 10 x - 18 = 0$
Which is not of the form $a x^{2} + b x + c$ , a $\neq$ 0. Thus the equation is not a quadratic equation.

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