Question

if x=2+√3, then find the value of x⁴-4x³+x²+x+1​

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Answer:

value of x¹ - 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

- 4x + 4 = 3

- 4x + 1 = 0. (1)

we have to find value of x² - 4x³ +; √3 X

= x²(x² - 4x + 1) + x - √3

from equation (1) we get,

= x² x 0 + x - √3

= 0 +(2+√3)-√3

= 2

if x=root[ 3+2 root 2] then find the value of x to the power 4+ 1/ x to the power 4