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 $10$

$x[4x^2+2x-8]+7$

$=\frac{\sqrt{3}+1}{2}[\frac{4}{4}\times (\sqrt{3}+1{)}^2+\frac{2}{2}(\sqrt{3}+1)-8]+7$

$=\frac{\sqrt{3}+1}{2}[4+2\sqrt{3}+\sqrt{3}+1-8]+7$

$=\frac{\sqrt{3}+1}{2}[3\sqrt{3}-3]+7=\frac{3}{2}\times 2+7=10$