Question

Solve for x :
$x+\frac{1}{x}=3,x\ne 0$

• A. $\frac{-3\pm \sqrt{5}}{3}$
• B. $\frac{3\pm \sqrt{5}}{2}$
• C. $\frac{-3\pm \sqrt{5}}{2}$
• D. $\frac{3\pm \sqrt{5}}{3}$

Answer 1

Answer: (B)

$\frac{3\pm \sqrt{5}}{2}$

$x+\frac{1}{x}=3$

$\Rightarrow$ $x^2+1=3x$

$\Rightarrow$ $x^2-3x+1=0$

$\Rightarrow$ Here, $a=1,b=-3,c=1$

$\Rightarrow$ $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$=\frac{-(-3)\pm \sqrt{(-3{)}^2-4(1\left)\right(1)}}{2\left(1\right)}$

$=\frac{3\pm \sqrt{9-4}}{2}$

$=\frac{3\pm \sqrt{5}}{2}$

$\therefore$ $x=\frac{3+\sqrt{5}}{2}$ and $x=\frac{3-\sqrt{5}}{2}$