Question

If x=1/2-√3 find the value of x^3-2x^2-7x-4

Answer 1

x=1/(2-√3)

Then; rationalise x,

x=(2+√3)/[(2-√3)(2+√3)

Or, x= (2+√3)/(4-3)

Or, x=2+√3

Now putting the value of x in the expression we get;

x^3 - 2x^2 - 7x +5

= (2 + √3)^3 - 2(2 + √3)^2 - 7(2 + √3) + 5

= (2 + √3) [(2 + √3)^2 - 2(2 + √3) - 7] + 5

= (2 + √3) [4 + 3 + 4√3 - 4 - 2√3 - 7] + 5

= (2 + √3) [-4 + 2√3] + 5

= -2(2 + √3)(2 - √3) + 5

= -2(1) + 5

= 3

the required and is 3


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