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The value of expression x^4-8x^3+18 x^2-...

The value of expression `x^4-8x^3+18 x^2-8x+2` when `x=2+sqrt(3)`

A

2

B

1

C

0

D

3

Text Solution

Verified by Experts

The correct Answer is:
B
`x = 2 + sqrt3`
or `(x - 2)^(2) = 3`
or `x^(2) - 4x + 1 = 0" "(1)`
or `(x - 2)^(4) = 9`
or `x^(4) - 8x^(3) + 24x^(2) - 32x + 16 = 9`
or `x^(4) - 8x^(3) + 18x^(2) - 8x + 2 + 6(x^(2) - 4x + 1) - 1 = 0`
Using (1), we get
`x^(4) - 8x^(3) + 18x^(2) - 8x + 2 = 1`
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Knowledge Check

  • The minimum value of function f(x)=3x^4-8x^3+12x^2-48x+25 on [0,3] is equal to

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    D
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    `5 `
    C
    `2x + 5 `
    D
    `2x - 5`

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