Quadratic Equation Question 3
Question 3 - 24 January - Shift 2
The number of real solutions of the equation $3(x^{2}+\frac{1}{x^{2}})-2(x+\frac{1}{x})+5=0$, is
(1) 4
(2) 0
(3) 3
(4) 2
Show Answer
Answer: (2)
Solution:
Formula: Roots of equations
$3(x^{2}+\frac{1}{x^{2}})-2(x+\frac{1}{x})+5=0$
$3[(x+\frac{1}{x})^{2}-2]-2(x+\frac{1}{x})+5=0$
Let $x+\frac{1}{x}=t$
$3 t^{2}-2 t-1=0$
$3 t^{2}-3 t+t-1=0$
$3 t(t-1)+1(t-1)=0$
$(t-1)(3 t+1)=0$
$t=1,-\frac{1}{3}$
$x+\frac{1}{x}=1,-\frac{1}{3} \Rightarrow$ No solution.
