Question

If x=1/2-root3 , find the value of x^3-2x^2-7x+5

Answer 1

Hello Mate!

$x = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \frac{2 + \sqrt{3} }{4 - 3} = 2 + \sqrt{3} \\ {x}^{3} = {(2 + \sqrt{3}) }^{3} \\ = 8 + 3 \sqrt{3} + 12 \sqrt{3} + 3 \times 2 \times { \sqrt{3} }^{2 } \\ = 8 + 15 \sqrt{3} + 18 \\ = 26 + 15 \sqrt{3} \\ 2 {x}^{2} = 2 {(2 + \sqrt{3} )}^{2} \\ 2(4 + 3 + 4 \sqrt{3} ) \\ 14 + 8 \sqrt{3} \\ 7x = 7(2 + \sqrt{3} ) = 14 + 7 \sqrt{3 } \\ 26 + 15 \sqrt{3} - (14 + 8 \sqrt{3} ) - (14 + 7 \sqrt{3} ) + 5 \\ 3 + \sqrt{ 3} (15 - 8 - 7) \\ 3 + \sqrt{3} (0) \\ 3$

Hope it helps☺!