Question

If $x^2-4x+2=0$, then the value of $4x^2+2x+\frac{4}{x}+\frac{16}{x^2}$ is

• A. $12$
• B. $16$
• C. $26$
• D. $56$

Answer 1

The correct option is D $56$

$x^2-4x+2=0\Rightarrow x+\frac{2}{x}=4$
Squaring both sides, we get
$\Rightarrow x^2+\frac{4}{x^2}+4=16\Rightarrow x^2+\frac{4}{x^2}=12$
Hence, $4x^2+2x+\frac{4}{x}+\frac{16}{x^2}=4(x^2+\frac{4}{x^2})+2(x+\frac{2}{x})$
$=4\times 12+2\times 4=56$.