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Algebraic Identities

If x2 + 2 =...

Question

If $x^{2} + 2 = 2 x$ , then the value of $x^{4} - x^{3} + x^{2} + 2$ is

0

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\sqrt{2}

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Solution

The correct option is A $0$
$x^{2} + 2 = 2 x \Rightarrow x^{2} - 2 x + 2 = 0 ⟶ 1$
To find
$x^{4} - x^{3} + x^{2} + 2 = x^{4} + 2 x^{3} + 2 x^{2} + x^{3} - x^{2} + 2 = (x^{4} - 2 x^{3} + 2 x^{2}) + (x^{3} - 2 x^{2} + 2 x) + (x^{2} - 2 x + 2) = x^{2} (x^{2} - 2 x + 2) + x (x^{2} - 2 x + 2) + (x^{2} - 2 x + 2) = x^{2} (0) + x (0) + 0 f r o m ⟶ 1 = 0$

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0 < | x | < \sqrt{2}

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