QJEEM23Ma7609: JEE Main 2023 Mathematics - Class 11 JEEM23Ma7609 Solution: The number of real solutions of the equation , is

Question

Verified Solution • 2025–26 Session moderate

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

Accepted Answer

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

Put

x+\frac{1}{x}=t \Rightarrow t \in(-\infty,-2] \cup[2, \infty)

\begin{aligned}&amp; 3 t^{2}-2 t-1=0 \\\\&amp; 3 t^{2}-3 t+t-1=0 \\\\&amp; \Rightarrow 3 t(t-1)+1(t-1)=0 \Rightarrow t=1,=-\frac{1}{3} \\\\&amp; \Rightarrow \quad t=1,-\frac{1}{3} \\\\&amp; \because t \in(-\infty,-2] \cup[2, \infty)\end{aligned}

No real value of

t \Rightarrow

no real value of

x

.

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