4-2.Quadratic Equations and Inequations
hard

સમીકરણ $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$ ના વાસ્તવિક ઉકેલોની સંખ્યા $.............$ છે.

A

$4$

B

$0$

C

$3$

D

$2$

(JEE MAIN-2023)

Solution

$3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$

$3\left[\left(x+\frac{1}{x}\right)^2-2\right]-2\left(x+\frac{1}{x}\right)+5=0$

Let $x +\frac{1}{ x }= t$

$3 t ^2-2 t -1=0$

$3 t ^2-3 t + t -1=0$

$3 t ( t -1)+1( t -1)=0$

$( t -1)(3 t +1)=0$

$t =1,-\frac{1}{3}$

$x +\frac{1}{ x }=1,-\frac{1}{3} \Rightarrow \text { No solution. }$

Standard 11
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.