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August 2022
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√(x+4,2)+1/√(x+4,2)≥5/2
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sedinalana
Verified answer
ОДЗ
x+4,2>0⇒x>-4,2
√(x+4,2)=a
a+1/a≥5/2
(2a²-5a+2)/a≥0
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=0,5
a2=(5+3)/4=2
a=0
_ + _ +
--------------(0)-----------[0,5]------------[2]--------------
0<a≤0,5⇒0<√(x+4,2)≤0,5⇒x+4,2≤0,25⇒x≤-3,95
a≥2⇒√(x+4,2)≥2⇒x+4,2≥4⇒x≥-0.2
x∈(-4,2;-3,95] U [-0,2;∞)
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Answers & Comments
Verified answer
ОДЗx+4,2>0⇒x>-4,2
√(x+4,2)=a
a+1/a≥5/2
(2a²-5a+2)/a≥0
2a²-5a+2=0
D=25-16=9
a1=(5-3)/4=0,5
a2=(5+3)/4=2
a=0
_ + _ +
--------------(0)-----------[0,5]------------[2]--------------
0<a≤0,5⇒0<√(x+4,2)≤0,5⇒x+4,2≤0,25⇒x≤-3,95
a≥2⇒√(x+4,2)≥2⇒x+4,2≥4⇒x≥-0.2
x∈(-4,2;-3,95] U [-0,2;∞)