Question

State true or false:

If $5m^2+m=3$, then $m=\frac{-1\pm \sqrt{61}}{10}$.

• A. True
• B. False

Answer 1

The correct option is A True

Given, $5m^2+m=3$
$\Rightarrow 5m^2+m-3=0$
$\Rightarrow m^2+\frac{1}{5}m-\frac{3}{5}=0$
$\Rightarrow {(m+\frac{1}{10})}^2-\frac{3}{5}-\frac{1}{100}=0$
$\Rightarrow {(m+\frac{1}{10})}^2-\left(\frac{60+1}{100}\right)=0$
$\Rightarrow {(m+\frac{1}{10})}^2=\frac{61}{100}$
$\Rightarrow m+\frac{1}{10}=\pm \frac{\sqrt{61}}{10}$
$\Rightarrow m=-\frac{1}{10}\pm \frac{\sqrt{61}}{10}$
$\Rightarrow m=\frac{-1\pm \sqrt{61}}{10}$