Предмет: Алгебра,
автор: pvlad01
решите неравенство)))
Приложения:
Ответы
Автор ответа:
2
Решим с помощью метода интервалов.
![1) (x-2)^2(x+1)(x-1)^2(x^2+2x+5)\ \textless \ 0 \\ \\
(x^2+2x+5)=0 \\ \\
D=4-4*1*5\ \textless \ 0 \\ \\
Znachit \;\; ne \;\; uchitovaem \\ \\
+++++[-1]-----[1^p]-----[2]+++++ \\ \\
\boxed {x\in (-1;1)U(1;2)} \\ \\ \\
2) \frac{(x-3)^2(x-2)x}{(x+1)^4(x+5)}\ \textgreater \ 0 \\ \\
---[-5]+++[-1^p]+++[0]---[-2]+++[3^p]+++ \\ \\
\boxed {x\in (-5;-1)U(-1;0)U(2;3)U(3;+\infty)} \\ \\ \\
3) \sqrt{x} (x+2)\ \textgreater \ 0 \\ \\
ODZ:\;x \geq 0 \\ \\
x\ \textgreater \ -2-ne \;\;vxodit \;\; v \;\; ODZ, \;\; znachi: \\ \\
\boxed {x\in (0;+\infty)}](https://tex.z-dn.net/?f=1%29+%28x-2%29%5E2%28x%2B1%29%28x-1%29%5E2%28x%5E2%2B2x%2B5%29%5C+%5Ctextless+%5C+0+%5C%5C++%5C%5C+%0A%28x%5E2%2B2x%2B5%29%3D0+%5C%5C++%5C%5C+%0AD%3D4-4%2A1%2A5%5C+%5Ctextless+%5C+0+%5C%5C++%5C%5C+%0AZnachit+%5C%3B%5C%3B+ne+%5C%3B%5C%3B+uchitovaem++%5C%5C++%5C%5C+%0A%2B%2B%2B%2B%2B%5B-1%5D-----%5B1%5Ep%5D-----%5B2%5D%2B%2B%2B%2B%2B+%5C%5C++%5C%5C+%0A%5Cboxed+%7Bx%5Cin+%28-1%3B1%29U%281%3B2%29%7D+%5C%5C++%5C%5C++%5C%5C+%0A2%29++%5Cfrac%7B%28x-3%29%5E2%28x-2%29x%7D%7B%28x%2B1%29%5E4%28x%2B5%29%7D%5C+%5Ctextgreater+%5C+0+%5C%5C++%5C%5C+%0A---%5B-5%5D%2B%2B%2B%5B-1%5Ep%5D%2B%2B%2B%5B0%5D---%5B-2%5D%2B%2B%2B%5B3%5Ep%5D%2B%2B%2B+%5C%5C++%5C%5C+%0A%5Cboxed+%7Bx%5Cin+%28-5%3B-1%29U%28-1%3B0%29U%282%3B3%29U%283%3B%2B%5Cinfty%29%7D++%5C%5C++%5C%5C++%5C%5C+%0A3%29++%5Csqrt%7Bx%7D+%28x%2B2%29%5C+%5Ctextgreater+%5C+0+%5C%5C++%5C%5C+%0AODZ%3A%5C%3Bx+%5Cgeq+0+%5C%5C++%5C%5C+%0Ax%5C+%5Ctextgreater+%5C+-2-ne+%5C%3B%5C%3Bvxodit+%5C%3B%5C%3B+v+%5C%3B%5C%3B+ODZ%2C+%5C%3B%5C%3B+znachi%3A+%5C%5C++%5C%5C%0A%5Cboxed+%7Bx%5Cin+%280%3B%2B%5Cinfty%29%7D "1) (x-2)^2(x+1)(x-1)^2(x^2+2x+5)\ \textless \ 0 \\ \\
(x^2+2x+5)=0 \\ \\
D=4-4*1*5\ \textless \ 0 \\ \\
Znachit \;\; ne \;\; uchitovaem \\ \\
+++++[-1]-----[1^p]-----[2]+++++ \\ \\
\boxed {x\in (-1;1)U(1;2)} \\ \\ \\
2) \frac{(x-3)^2(x-2)x}{(x+1)^4(x+5)}\ \textgreater \ 0 \\ \\
---[-5]+++[-1^p]+++[0]---[-2]+++[3^p]+++ \\ \\
\boxed {x\in (-5;-1)U(-1;0)U(2;3)U(3;+\infty)} \\ \\ \\
3) \sqrt{x} (x+2)\ \textgreater \ 0 \\ \\
ODZ:\;x \geq 0 \\ \\
x\ \textgreater \ -2-ne \;\;vxodit \;\; v \;\; ODZ, \;\; znachi: \\ \\
\boxed {x\in (0;+\infty)}")
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