Question

The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is

• A. 4
• B. 3
• C. 2
• D. 0

Answer 1

Answer: (D)

$3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$
$3\left[{\left(x+\frac{1}{x}\right)}^2-2\right]-2\left(x+\frac{1}{x}\right)+5=0$
Let $x+\frac{1}{x}=t$
$3t^2-2t-1=0$
$3t^2-3t+t-1=0$
$3t(t-1)+1(t-1)=0$
$(t-1)(3t+1)=0$
$t=1,-\frac{1}{3}$
$x+\frac{1}{x}=1,-\frac{1}{3}\Rightarrow$ No solution.