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IPMAT Indore 2023 - QA (MCQ) Q21 Explanation
December 30, 2024
Explanation:
(d)
𝑥^2(𝑥+1)/(𝑥−1)(2𝑥+1)^3 > 0
As, denominator can’t be equal to zero. ∴ x ≠ 1, −1/2
Multiplying both side of inequality by an expression (𝑥−1)^2(2𝑥+1)^4/𝑥2 , a perfect square whose value is always positive, we get
𝑥^2(x+1)/(𝑥−1)(2𝑥+1)^3 × (𝑥−1)^2(2𝑥+1)^4/𝑥2 > 0 × (𝑥−1)^2(2𝑥−1)^4/𝑥2
= (x+1) (x-1) (2x+1) > 0
Solving the above inequality using Wavy Curve method,
x ∈ (-1, −1/2) ∪ (1, +∞) Ans.