The solution set of the inequation x2+6x+5>8-x is

Given inequation x2+6x+5 > (8−x)⇒ x2+6x+5>0 and x2+6x+5> (8−x)2Case(i): x2+6x+5>0⇒ (x+1)(x+5)>0∴ x −1Case(ii): x2+6x+5>(8−x)2⇒ x2+6x+5>64+x2−16x⇒ 22x>59⇒ x> 5922∴ x∈ (5922, ∞)

The solution set of the inequation x2+6x+5>8-x is

Given inequation x2+6x+5 > (8−x)⇒ x2+6x+5>0 and x2+6x+5> (8−x)2Case(i): x2+6x+5>0⇒ (x+1)(x+5)>0∴ x −1Case(ii): x2+6x+5>(8−x)2⇒ x2+6x+5>64+x2−16x⇒ 22x>59⇒ x> 5922∴ x∈ (5922, ∞)

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

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

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$(8, \infty)$

$(\frac{55}{22}, 8]$

$(\frac{59}{22}, \infty]$

$(1, \infty)$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} G i v e n i n e q u a t i o n \sqrt{x^{2} + 6 x + 5} > (8 - x) \\ \Rightarrow x^{2} + 6 x + 5 > 0 a n d x^{2} + 6 x + 5 > {(8 - x)}^{2} \\ C a s e (i) : x^{2} + 6 x + 5 > 0 \\ \Rightarrow (x + 1) (x + 5) > 0 \\ ∴ x < - 5 o r x > - 1 \\ C a s e (i i) : x^{2} + 6 x + 5 > {(8 - x)}^{2} \\ \Rightarrow x^{2} + 6 x + 5 > 64 + x^{2} - 16 x \\ \Rightarrow 22 x > 59 \\ \Rightarrow x > \frac{59}{22} \\ ∴ x \in (\frac{59}{22}, \infty) \end{array}$