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If x=1/(2-sqrt(3)), find the value of x^...

If `x=1/(2-sqrt(3)),` find the value of `x^3-2x^2-7x+5`

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The correct Answer is:
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We have,
`x=(1)/(2-sqrt(3))=(1)/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3))=(2+sqrt(3))/((2)^(2)-(sqrt(3))^(2))=2+sqrt(3)`
`rArr" "(x-2)=sqrt(3)`
Squaring both sides, we get
`(x-2)^(2)=(sqrt(3))^(2)`
`rArr" "x^(2)-4x+4=3`
`rArr" "x^(2)-4x+1=0` . . . (1)
`"Now, "x^(3)-2x^(2)-7x+5=x(x^(2)-4x+1)+2x^(2)-8x+5`
`=x(x^(2)-4x+1)+2(x^(2)-4x+1)+3`
`-x(0)+2(0)+3` [from (1)]
= 3
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