TS EAMCET · Maths · Basic of Mathematics
The set of values of \(x\) for which the inequalities \(x^2-3 x-10 < 0, \quad 10 x-x^2-16>0 \quad\) hold simultaneously, is
- A \((-2,5)\)
- B \((2,8)\)
- C \((-2,8)\)
- D \((2,5)\)
Answer & Solution
Correct Answer
(D) \((2,5)\)
Step-by-step Solution
Detailed explanation
Given inequalities are \(\begin{array}{lll}x^2-3 x-10 \\ \Rightarrow x^2-5 x+2 x-10 0 \\ \Rightarrow x^2-10 x+16 < 0 \\ \Rightarrow x^2-8 x-2 x+16 < 0 \\ \Rightarrow (x-2)(x-8) < 0 \\ \Rightarrow x \in(-2,5) \cap(2,8) \\ \therefore x \in(2,5)\end{array}\)
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