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JEE Main

Exam: JEE Main
Subject: Mathematics
Chapter: Basics of Mathematics

JEE Main · Mathematics · Basics of Mathematics

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

The solution set of the inequation

\sqrt{x^2+6 x+5}>(8-x)

is

Options

A $(8, \infty)$
B $\left(\frac{59}{22}, 8\right]$
C $\left(\frac{59}{22}, \infty\right)$
D $(-1, \infty)$

Correct answer

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

Step-by-step solution

\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 \\ x²+6 x+5>64-16 x+x² \\ 6 x+16 x>64-5 \\ 22 x>59 \\ x>\frac{59}{22}\\ x \in\left(\frac{59}{22}, \infty\right) \end{gathered}

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