TS EAMCET · Maths · Basic of Mathematics
The solution set of the inequation \(\sqrt{x^2+x-2}\gt(1-x)\) is
- A \((-\infty, 2)\)
- B \((-\infty,-2)\)
- C \((1, \infty)\)
- D \((0, \infty)\)
Answer & Solution
Correct Answer
(C) \((1, \infty)\)
Step-by-step Solution
Detailed explanation
\(x^2+x-2\gt0 \Rightarrow(x+2)(x-1)\gt0 \Rightarrow x\gt1, x \lt -2\) If \(x\gt1\) \(1-x \lt 0\) and \(\sqrt{x^2+x-2}\gt0 \Rightarrow \sqrt{x^2+x-2}\gt1-x\) If \(x \lt -2\) \(\sqrt{x^2+x-2}\gt0\) and \(1-x\gt0 \Rightarrow \sqrt{x^2+x-2}\gt(1-x)\)…
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