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AP EAMCET · Maths · Basic of Mathematics

The solution set of the inequation \(\sqrt{x^2+6 x+5}>(8-x)\) is

  1. A \((8, \infty)\)
  2. B \(\left(\frac{59}{22}, 8\right]\)
  3. C \(\left(\frac{59}{22}, \infty\right)\)
  4. D \((-1, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left(\frac{59}{22}, \infty\right)\)

Step-by-step Solution

Detailed explanation

\(\sqrt{x^2+6 x+5}>(8-x)\) On squaring both side, \(\begin{gathered} \left(\sqrt{x^2+6 x+5}\right)^2>(8-x)^2 \\ x^2+6 x+5>64-16 x+x^2 \\ 6 x+16 x>64-5 \\ 22 x>59 \\ x>\frac{59}{22} \\ x \in\left(\frac{59}{22}, \infty\right) \end{gathered}\)