Question

Solve the following quadratic equation using quadratic formula: $x+\frac{1}{x}=2\frac{1}{2}$

• A. $\{\frac{1}{2},2\}$
• B. $\{\frac{1}{2},-2\}$
• C. $\{\frac{-1}{2},2\}$
• D. None of these

Answer 1

Answer: (A)

$\{\frac{1}{2},2\}$

Given equation is $x+\frac{1}{x}=2\frac{1}{2}$

$\Rightarrow$ $\frac{x^2+1}{x}=\frac{5}{2}$

$\Rightarrow$ $2(x^2+1)=5x$

$\Rightarrow$ $2x^2+2=5x$

$\Rightarrow$ $2x^2-5x+2=0$

$\Rightarrow$ Here, $a=2,b=-5,c=2$

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

$=\frac{-(-5)\pm \sqrt{(-5{)}^2-4(2\left)\right(2)}}{2\left(2\right)}$

$=\frac{5\pm \sqrt{25-16}}{4}$

$=\frac{5\pm \sqrt{9}}{4}$

$=\frac{5\pm 3}{4}$

$\Rightarrow$ $x=\frac{5+3}{4}$ and $x=\frac{5-3}{4}$

$\therefore$ $x=2$ and $x=\frac{1}{2}$