How to solve 13th question Q13 The solution set of the inequation log1/3 (x2 + x + 1) - Maths - Relations and Functions

Question

How to solve 13th question

Q13 The solution set of the inequation log1/3
(x2 + x + 1) + 1 > 0 is

(A) (– ∞ , –2) ◡ (1, + ∞ )

(B) [–1, 2]

(C) (–2, 1)

(D) (– ∞ + ∞ )

Shruti Tyagi · Accepted Answer

Dear Student, Please find below the solution log13x2+x+1+1>0⇒log13x2+x+1>-1as we know logab=c gives ac=b⇒x2+x+1>13-1⇒x2+x+1>3⇒x2+x+1-3>0⇒x2+x-2>0⇒x2+2x-x-2>0⇒xx+2-1x+2>0⇒x-1x+2>0therefore x-1>0 and x+2>0or x-1<0 and x+2<0⇒x>1 and x>-2 or x<1 and x<-2the common set of the above conditionx<-2 and x>1Hence the solution set of given problem is x∈-∞,-2∪1,∞ Regards,

How to solve 13th question Q13. The solution set of the inequation log1/3 (x2 + x + 1) + 1 > 0 is (A) (– ∞ , –2) ◡ (1, + ∞ ) (B) [–1, 2] (C) (–2, 1) (D) (– ∞ + ∞ )

How to solve 13th question

Q13. The solution set of the inequation log_1/3 (x² + x + 1) + 1 > 0 is

(A) (– $\infty$ , –2) $◡$ (1, + $\infty$ )

(B) [–1, 2]

(C) (–2, 1)

(D) (– $\infty$ + $\infty$ )