Question

The roots of the equation $x+\frac{1}{x}=3,x\ne 0$ are

• A. $\frac{3+\sqrt{7}}{2},\frac{3-\sqrt{7}}{2}$
• B. $\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$
• C. $\frac{-3+\sqrt{5}}{2},\frac{-3-\sqrt{5}}{2}$
• D. $\frac{-3+\sqrt{7}}{2},\frac{-3-\sqrt{7}}{2}$

Answer 1

The correct option is B $\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}$

Given,
$x+\frac{1}{x}=3\Rightarrow x^2+1=3x\Rightarrow x^2-3x+1=0$
Using quadratic formula, we get
$x=\frac{-b\pm \sqrt{D}}{2a}\Rightarrow x=\frac{3\pm \sqrt{9-4}}{2}$

Hence, the roots are
$\frac{3+\sqrt{5}}{2}$ and $\frac{3-\sqrt{5}}{2}$