If x = 1 + √ 2, then what is the value of x 4 - 4x 3 + 4x 2?

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Accepted Answer

x = 1 + √2 ∴ x4 - 4x3 + 4x2 = x2(x2 - 4x + 4) = x2(x - 2)2 = (1 + √2)2(1 + √2 - 2)2 =(√2 + 1)2 (√2 - 1)2 =[(√2)2 - (1)2]2 =(2 - 1)2 =1

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