Question

The roots of the equation $a(x^2+1)-(a^2+1)x=0$ are:

• A. $a,\frac{1}{a}$
• B. $a,2a$
• C. $a,\frac{1}{2a}$
• D. none of these

Answer 1

Answer: (A)

We have
$a\left(x^2+1\right)-\left(a^2+1\right)x=0$
$\Rightarrow a{x}^2-\left(a^2+1\right)x+a=0$
$\Rightarrow \left(a{x}^2-a^{2}x\right)-(x-a)=0$
$\Rightarrow ax(x-a)-1(x-a)=0$
$\Rightarrow (x-a)(ax-1)=0$
$\Rightarrow x=a,\frac{1}{a}$