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cemmmka92
@cemmmka92
April 2021
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Решите неравенство V(a+x) + V(a-x) >a при всех значениях параметра а.
П.С.: V - корень квадратный
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Checov7400
А+х+2√(а²-х²)+а-х=2а+2√(а²-х²)
2а+2√(а²-х²)>a a+2√(a²-x²)>0
(a²)>(-2√(a²-x²))² a²>4a²-x² x²-3a²>0 (x-√3 *a)(x+√3 *a)>0
x- √3 a =0 x=√3a
x+√3 a=0 x=-√3 a
------------ -√3a-----------------√3a----------- x
+ - +
x∈(-∞; -√3а)∪(√3а;+∞)
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Answers & Comments
2а+2√(а²-х²)>a a+2√(a²-x²)>0
(a²)>(-2√(a²-x²))² a²>4a²-x² x²-3a²>0 (x-√3 *a)(x+√3 *a)>0
x- √3 a =0 x=√3a
x+√3 a=0 x=-√3 a
------------ -√3a-----------------√3a----------- x
+ - +
x∈(-∞; -√3а)∪(√3а;+∞)