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

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

C

Explanation

If `x = (1)/(2-sqrt(3))`, then the …………..
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))/(4-3) = 2 + sqrt(3)`
`implies x - 2 = sqrt(3)`
`implies (x-2)^(2) = (sqrt(3))^(2)`
`implies x^(2)-4x+4=3`
`implies x^(2)-4x+1 = 0` ............... (i)
`:. x^(2)-2x^(2)-7x+5`
`= x(x^(2)-4x+1)+2(x^(2)-4x+1)+3`
`= 3` [using (i)]