The number of real solutions of the equation tan⁻¹(x−1) + tan⁻¹(x) + tan⁻¹(x+1) = tan⁻¹(3x) is:
The number of real solutions of the equation tan⁻¹(x−1) + tan⁻¹(x) + tan⁻¹(x+1) = tan⁻¹(3x) is:
- A. 0
- B. 1
- C. 2
- D. 3
Answer: D) 3
Explanation: tan⁻¹(x−1) + tan⁻¹(x+1) = tan⁻¹(3x) − tan⁻¹(x). Applying the formula yields 2x / (2−x²) = 2x / (1+3x²). Roots are x=0 and 2−x² = 1+3x² → x=±1/2. Exactly 3 real solutions.
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