Question

If $x=\frac{\sqrt{3}+1}{2}$, then the value of $4x^3+2x^2-8x+7$ is ___.

• A. $10$
• B. $8$
• C. $6$
• D. $4$

Answer 1

The correct option is A $10$

$\Rightarrow 4x^2-4x-2=0\dots$ eqn(1)

Now we have, $4x^3+2x^2-8x+7$

Above can be written as

$x(4x^2-4x-2+6x-6)+7$

$=x(0+6x-6)+7$ (from eqn(1))

$=6x^2-6x+7$

$=6(x^2-x)+7$

$=\frac{6}{4}(4x^2-4x-2+2)+7$

$=\frac{6}{4}(0+2)+7$ (from eqn (1))

$=3+7=10$