cat 2020 Question 11

Question

The number of distinct real roots of the equation $(x + \frac{1}{x})^{2}$ - 3(x + $\frac{1}{x}$ ) + 2 = 0 equals

Accepted Answer

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

So, the given equation is $a^2 - 3a + 2 = 0$

So, $a$ can be either $2$ or $1$.

If $a = 1$, $x + \frac{1}{x} = 1$ and it has no real roots.

If $a = 2$, $x + \frac{1}{x} = 2$ and it has exactly one real root which is $x = 1$.

So, the total number of distinct real roots of the given equation is 1

Question 11.