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x-4-2-2-x-4-x-4-

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Question Number 163222 by cortano1 last updated on 05/Jan/22
(√(((√(x+4)) +2)/(2−(√(x+4))))) ≤ x−4
x+4+22−x+4⩽x−4
Answered by blackmamba last updated on 05/Jan/22
no solution for x∈R (1) x−4>0⇒x>4 (2) (((√(x+4))+2)/(2−(√(x+4)))) ≥0 ; (√(x+4)) = t ((t+2)/(2−t)) ≥0 ⇒ ((t+2)/(t−2)) ≤0 ⇒−2≤t<2 −2≤(√(x+4)) <2 ⇒(√(x+4)) < 2 x <0 ; (1)∩(2)=∅
nosolutionforx∈R(1)x−4>0⇒x>4(2)x+4+22−x+4⩾0;x+4=tt+22−t⩾0⇒t+2t−2⩽0⇒−2⩽t<2−2⩽x+4<2⇒x+4<2x<0;(1)∩(2)=∅

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