Question:
Which of the following is not a quadratic equation?
(a) $3 x-x^{2}=x^{2}+5$
(b) $(x+2)^{2}=2\left(x^{2}-5\right)$
(c) $(\sqrt{2} x+3)^{2}=2 x^{2}+6$
(d) $(x-1)^{2}=3 x^{2}+x-2$
Solution:
(c) $(\sqrt{2} x+3)^{2}=2 x^{2}+6$
$\because(\sqrt{2} x+3)^{2}=2 x^{2}+6$
$\Rightarrow 2 x^{2}+9+6 \sqrt{2} x=2 x^{2}+6$
$\Rightarrow 6 \sqrt{2} x+3=0$, which is not a quadratic equation