Question

(х-1)в кубе-(х+1)в кубе больше х-6хв квадрате (х+5)(х-+3)х больше х+1 решить неравенство

Answer 1

1 неравенство. 
$(x-1)^3-(x+1)^3\ \textgreater \ x-6x^2\\(x-1-(x+1))((x-1)^2+(x-1)(x+1)+(x+1)^2)\ \textgreater \ x-6x^2\\-2(x^2-2x+1+x^2-1+x^2+2x+1)\ \textgreater \ x-6x^2\\-2(3x^2+1)\ \textgreater \ x-6x^2\ \textless \ =\ \textgreater \ -6x^2-2\ \textgreater \ x-6x^2\\-2\ \textgreater \ x\ \textless \ =\ \textgreater \ x\ \textless \ -2$

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где $\alpha=-2$, $\beta=0$.
ответ: x∈(–∞; –2). 

2 неравенство. 
$(x+5)(x-5)-(x+3)x\ \textgreater \ x+1\\x^2-25-x^2-3x\ \textgreater \ x+1\\-3x-25\ \textgreater \ x+1\ \textless \ =\ \textgreater \ 3x+25\ \textgreater \ -x-1\\4x\ \textgreater \ -26\\x\ \textgreater \ -6,5$
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где $\alpha=-6,5$, $\beta=0$.
ответ: x∈(–6,5; +∞).