Question

# The value of the expression $$x^4-8x^3+18x^2-8x+2$$ when $$x=2+\sqrt 3$$

A
2
B
1
C
0
D
3

Solution

## The correct option is B $$1$$$$x=2+\sqrt { 3 } \\$$ or$$\quad { (x-2) }^{ 2 }={ (\sqrt { 3 } ) }^{ 2 }\\$$ or$$\quad { x }^{ 2 }-4x+1=0\\$$ or$$\quad { (x-2) }^{ 4 }=9\\$$ or$$\quad { x }^{ 4 }-8{ x }^{ 3 }+24{ x }^{ 2 }-32x+16=9\\$$ or$$\quad { x }^{ 4 }-8{ x }^{ 3 }+18{ x }^{ 2 }-8x+2+6({ x }^{ 2 }-4x+1)-1=0\\$$As$$\quad { x }^{ 2 }-4x+1=0,\quad$$ we get,$$\\ { x }^{ 4 }-8{ x }^{ 3 }+18{ x }^{ 2 }-8x+2=1$$Mathematics

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