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

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

A. -1

B. 1

C. 0

D. 2

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

This Question Belongs to Arithmetic Ability >> Algebra

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