Question

if x is equal to 1 divided by 2 minus root 3 find the value of x cube minus 2 x square - 7 x + 5 ​

Answer 1

Answer:

X=1/2-√3

X square=(1/2-√3) square

=1/4+3-√3

then,

2(x) square-7x+5=2(1/4+3-√3)-7(1/2-√3)+5

1/2+6-2√3-7/2+7√3+5

=-6/2+11+5√3

Answer 2

given : $x = \frac{1}{2-\sqrt{3}}$

to find : $x^3-2x^2-7x+5$

solution :

first we simplify the value of x

$x = \frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}= 2+\sqrt{3}$

now , finding x²

we get

$x^2 = \left ( \frac{1}{2-\sqrt{3}} \right )^2= \frac{1}{(2-\sqrt{3})^2}\\\\\frac{1}{4+3-4\sqrt{3}}= \frac{1}{7-4\sqrt{3}}\times \frac{7+4\sqrt{3}}{7+4\sqrt{3}}\\\\x^2 = 7+4\sqrt{3}$

now we find x³

$x^3 = x^2 \times x \\\\(2+\sqrt{3})\times (7+4\sqrt{3})\\\\= 26+15\sqrt{3}$

now ,

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

$(26+15\sqrt{3})- 2(7+4\sqrt{3})-7(2+\sqrt{3})+5\\\\26+ 15\sqrt{3}-14-8\sqrt{3}-14-7\sqrt{3}+5\\\\=3$

hence , The value of $x^3-2x^2-7x+5$ is 3