Question

If x = 2+root 3 find the value of x raised to the power 4 - 4x cube + x square + x - root 3

Answer 1

value of x⁴ - 4x³ + x² + x - √3 = 2

it is given that, x = 2 + √3

⇒(x - 2) = √3

squaring both sides we get,

⇒(x - 2)² = (√3)²

⇒x² - 4x + 4 = 3

⇒x² - 4x + 1 = 0.......(1)

we have to find value of x⁴ - 4x³ + x² + x - √3

= x²(x² - 4x + 1) + x - √3

from equation (1) we get,

= x² × 0 + x - √3

= 0 + (2 + √3 ) - √3

= 2

hence, x⁴ - 4x³ + x² + x - √3 = 2

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Answer 2

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