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If x = 2 + 3 then find the value of...

This question belongs to Arithmetic Ability Algebra
Algebra
?

If x = 2 + √3, then find the value of x4 - 8x3 + 16x2.

Answer & Solution
Correct Answer: Option B
x = 2 + √3
x2 = 7 + 4√3
x4 - 8x3 + 16x2
= x2(x2 - 8x + 16)
= x2(x - 4)2
= (7 + 4√3)(2 + √3 - 4)2
= (7 + 4√3)(2 - √3)2
= (7 + 4√3)(7 - 4√3)
= 1
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