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au456
@au456
July 2022
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√(4-4x^3+x^6)>2(x+1)
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Verified answer
√(4-4x^3+x^6)>2(x+1)
д=16-4*4=0
√((x^3-2)^2)>2(x+1)
|x^3-2|>2(x+1)
при x^3>=2 |x^3-2|=x^3-2
x^3-2>2(x+1)
x^3-2x-4>0
x^3-2x^2+2x^2-4x+2x-4>0
(x-2)(x^2+2x+2)>0
(x-2)(x^2+2x+1+1)>0
(x-2)((x+1)^2+1)>0
(x-2)>0
x>2 (x^3>2) => x>2
при x^3<2 |x^3-2|=-x^3+2
-x^3+2>2(x+1)
-x^3-2x>0
x^3+2x<0
x*(x^2+2)<0
x<0 (x^3<2) => x<0
ответ x =(-беск;0) U (2;+ беск)
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Answers & Comments
Verified answer
√(4-4x^3+x^6)>2(x+1)д=16-4*4=0
√((x^3-2)^2)>2(x+1)
|x^3-2|>2(x+1)
при x^3>=2 |x^3-2|=x^3-2
x^3-2>2(x+1)
x^3-2x-4>0
x^3-2x^2+2x^2-4x+2x-4>0
(x-2)(x^2+2x+2)>0
(x-2)(x^2+2x+1+1)>0
(x-2)((x+1)^2+1)>0
(x-2)>0
x>2 (x^3>2) => x>2
при x^3<2 |x^3-2|=-x^3+2
-x^3+2>2(x+1)
-x^3-2x>0
x^3+2x<0
x*(x^2+2)<0
x<0 (x^3<2) => x<0
ответ x =(-беск;0) U (2;+ беск)