Question

The value of $x$ which satisfies the equality $|x^2+x-1|=2x-1$ for $x$ and inequality $x<\sqrt{3}$ is

• A. $-1$
• B. $1$
• C. $\frac{3}{2}$
• D. $-\frac{3}{2}$

Answer 1

The correct option is B $1$

$|x^2+x-1|=2x-1$ ......(1)
case 1:
$x^2+x-1=2x-1$
$\Rightarrow x^2-x=0$
$\Rightarrow x=0,1$
But $x=0$ does not satisfy (1)
case 2:
$x^2+x-1=-2x+1$
$\Rightarrow x^2+3x-2=0$
$\Rightarrow x=\frac{-3\pm \sqrt{17}}{2}$