Question

Solve for $2(x^2+\frac{1}{x^2})-9(x+\frac{1}{x})+14=0$

• A. $\frac{1}{2},1,2$
• B. $\frac{1}{2},1,-2$
• C. $\frac{1}{2},1,4$
• D. $\frac{1}{2},1,-4$

Answer 1

The correct option is A $\frac{1}{2},1,2$

Rewriting the equation :

$2\left(\right(x+\frac{1}{x}{)}^2-2)-9(x+\frac{1}{x})+14=0$

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

$\Rightarrow 2t^2-9t+10=0$

$\Rightarrow 2t^2-5t-4t+10=0$

$\Rightarrow t(2t-5)-2(2t-5)=0$

$\Rightarrow (2t-5)(t-2)=0$

$\therefore t=5/2ort=2$

$\Rightarrow x+(1/x)=5/2 or 2

Let x+(1/x)=5/2

$\Rightarrow 2x^2-5x+2=0$

$\Rightarrow 2x^2-4x-x+2=0$

$\Rightarrow (2x-1)(x-2)=0$$

$\therefore$ x=1/2 or x=2

Now let x+(1/x)=2

$\Rightarrow$x=1

Hence option "A" is correct