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Variable Separable Method

If x2+1=0 v...

Question

If $x^{2} + 1 = 0$ value of $x^{18} + x^{12} + x^{6} + 1$

A

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Solution

The correct option is A $0$
Given $x^{2} + 1 = 0$ ........(1).
Now,
$x^{18} + x^{12} + x^{6} + 1$
$= x^{12} (x^{6} + 1) + 1 (x^{6} + 1)$
$= (x^{12} + 1) (x^{6} + 1)$
$= (x^{12} + 1) (x^{2} + 1) (x^{4} - x^{2} + 1)$
$= 0$ . [ Using (1)]

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