TS EAMCET · Maths · Basic of Mathematics
The number of integral values of \(x\) satisfying \(9 x-2 < (x+2)^2 < 12 x-3\) is
- A not finite
- B 3
- C 4
- D 5
Answer & Solution
Correct Answer
(B) 3
Step-by-step Solution
Detailed explanation
We have, \(9 x-2 < (x+2)^2 < 12 x-3\) \(\begin{aligned} & \text { Case I } 9 x-2 < x^2+4 x+4 \\ & \qquad x^2-5 x+6>0 \Rightarrow(x-3)(x-2)>0\end{aligned}\) \(x \in(-\infty, 2) \cup(3, \infty)\) ...(i) Case II \(x^2+4 x+4 < 12 x-3\) \(x^2-8 x+7 < 0 \Rightarrow(x-7)(x-1) < 0\)…
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