Question

Solve: $(4x+2)\sqrt{x^2+x+1}=0$. The sum of values of x satisfying the above equation is $\frac{-a}{b}$ where $a,b$ are co-prime. Find $a+b$

Answer 1

$\left(4x+2\right)\sqrt{x^2+x+1}=0$

$\Rightarrow 4x+2=0$ (since $\sqrt{x^2+x+1}=0$ has Imaginary roots)

$\Rightarrow x=-\frac{2}{4}$

Sum of values of $x$ satisfying above equation $=-\frac{2}{4}=-\frac{1}{2}$ (since $1$ and $2$ are co-prime)

so, $a=1$ and $b=2$

and $a+b=3$