First slide

Introduction to ITF

Question

The number of solutions of the equation $2 \sin^{- 1} \sqrt{x^{2} - x + 1} + \cos^{- 1} (\sqrt{x^{2} - x}) = \frac{3 π}{2}$ is

Moderate

A

0
B

infinite
C

2
D

4

Solution

sin^–1x, cos^–1x are defined for x ≤ 1 and x ≥ 0
$\begin{array}{l} ∴ \sqrt{x^{2} - x + 1} < 1 and \sqrt{x^{2} - x} > 0 \\ \Rightarrow x^{2} - x \leq 0 and x^{2} - x \geq 0 \Rightarrow x^{2} - x = 0 \\ \Rightarrow x = 1, 0 \end{array}$
∴ There are two solutions, both satisfy the equation.

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