NinetynineCAT 2020 Slot 1 QA Q11 Equations
Question 11 of the Quantitative Ability (QA) section, CAT 2020 Slot 1, with CAT's official answer and a worked solution.
The number of distinct real roots of the equation
(x + \(\frac{1}{x}\))2 - 3(x + \(\frac{1}{x}\)) + 2 = 0 equals
(x + \(\frac{1}{x}\))2 - 3(x + \(\frac{1}{x}\)) + 2 = 0 equals
TITA: type in the answer. There are no options and no negative marking.
Answer: 1 Equations TITA
Solution
- Let \(t = x+\frac1x\): \(t^2-3t+2=0\), so \(t=1\) or \(t=2\).
- For real x, \(|t|\ge2\), so \(t=1\) gives nothing. \(t=2\) gives \(x=1\).
- Exactly 1 distinct real root.