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  1. If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 ?
    1. -1
    2. 0
    3. 1
    4. 2
Correct Option: C

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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