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Class-9»Maths

If x² + 2 = 2x, then find the value of x⁴ - x³ + x² + 2. Also show the method please.

$x^{4} - x^{3} + x^{2} + 2 = {(x^{2})}^{2} - x (x^{2}) + x^{2} + 2 = {(2 x - 2)}^{2} - x (2 x - 2) + (2 x - 2) + 2 (g i v e n, x^{2} + 2 = 2 x \Rightarrow x^{2} = 2 x - 2) = 4 x^{2} + 4 - 8 x - 2 x^{2} + 2 x + 2 x - 2 + 2 = 2 x^{2} - 4 x + 4 = 2 (x^{2} - 2 x + 2) = 2 \times 0 = 0 (g i v e n, x^{2} + 2 = 2 x \Rightarrow x^{2} + 2 - 2 x = 0) H e n c e, x^{4} - x^{3} + x^{2} + 2 = 0$

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