Question Number 100385 by bobhans last updated on 26/Jun/20

find the solution set of inequality  (((x^2 −9)(√(x+2)))/(x+(√((x+2)^2 )))) ≤ 0

Commented bybobhans last updated on 26/Jun/20

(1) x ≥−2    (2) x ≠ −1   (3) (√(x+2)) ≥ 0  ⇒ (x+3)(x−3)(x+∣x+2∣) ≤ 0  since x≥−2 then ∣x+2∣ = x+2  ⇒(x+3)(x−3)(2x+2) ≤ 0  (x+3)(x−3)(x+1) ≤ 0 ; x ≤ −3 ∪ −1< x ≤ 3 (4)  the solution set we get (1)∩(2)∩(4)  ⇔ −1 < x ≤ 3 ■

Commented bybemath last updated on 26/Jun/20

cooll

Answered by MJS last updated on 26/Jun/20

(((x^2 −9)(√(x+2)))/(x+∣x+2∣))≤0  defined for x≥−2∧x≠−1  ⇒ −1<x≤3  because x^2 −9≤0 for −3≤x≤3  and x+∣x+2∣≤0 for x≤−1

Commented bybemath last updated on 26/Jun/20

great prof. thank much