If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 4?  Choose the most appropriate option
A) -1  B) 0  C) 5  D) 2  E) 3
Answer   x = 1 + √2   ∴ x4 - 4x3 + 4x2 + 5 = x2(x2 - 4x + 4) + 4   = x2(x - 2)2 + 4   = (1 + √2)2(1 + √2 - 2)2 + 4   =(√2 + 1)2 (√2 - 1)2 + 4   =[(√2)2 - (1)2]2 + 4   =(2 - 1)2 =1 + 4= 
<gadget id="calculator">1 + 4</gadget>
<output>5</output>
5   5orrect Option: 5
<result>C</result>
If x = 1 + √2, then what is the value of x4 - 4x3 + 4x2 + 4?