Posted by **pavatharani** on Wednesday, August 3, 2011 at 11:51am.

if x=1/(2-3^1/2)

prove that

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

- maths -
**Reiny**, Wednesday, August 3, 2011 at 1:19pm
start with the equation:

x^3 - 2x^2 - 7x + 2 = 0

after two tries, I found x = -2 to be a solution

so it factors to

(x+2)(x^2-4x+1) = 0

from the second ...

x = (4 ± √12)/2 = 2 ± √3

but you told me x = 1/(2-√3)

rationalizing this ...

1/(2-√3) * (2+√3)/(2+√3)

= (2+√3)/(4 - 3) = 2 + √3

which is one of the values for x I got by solving the equation.

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