2. неравенство (х - а)(2х + 1)(х + b) > 0 имеет решение ( -1/2; -1) ∪ (3; +∞ ). найдите значения a, b.. Created by ninjakonohi007. algebra-ru

2; -1) ∪ (3; +∞ ). найдите значения a, b....

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2. неравенство (х - а)(2х + 1)(х + b) > 0 имеет решение ( -1/2; -1) ∪ (3; +∞ ). найдите значения a, b.

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$(x-a)(2x+1)(x+b)>0\\\\x\in (-\frac{1}{2};1)\cup (3;+\infty )\ \ \Rightarrow\ \ \ ---(-\frac{1}{2})+++(1)---(3)+++\ \ \Rightarrow \\\\(x+\frac{1}{2})(2x+1)(x-3)>0\\\\a)\ \ x-a=x+\frac{1}{2}\ \ ,\ \ -a=0,5\ \ ,\ \ a=-0,5\\\\{}\ \ \ \ x+b=x-3\ \ ,\ \ b=-3\\\\b)\ \ x-a=x-3\ \ ,\ \ -a=-3\ \ ,\ \ a=3\\\\{}\ \ \ \ x+b=x+\frac{1}{2}\ \ ,\ \ b=0,5\\\\Otvet:\ \ a)\ a=-0,5\ ,\ b=-3\ \ \ \ ili\ \ \ \ b)\ a=3\ ,\ b=0,5\ .$

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