Rozwiąż równanie:
-2x^3 - 2x + 4 = 0
-2x^3 - 2x + 4 = 0
Mathēmatikós
![-2x^{3}-2x+4=0 \\ \\ 2x^{3} + 2x - 4=0 \\ \\ 2x^{3} - 2x^{2} + 2x^{2} + 2x - 4=0 \\ \\ 2x^{2}(x-1) + 2(x^{2} + x -2) = 0 \\ \\ 2x^{2}(x-1) + 2(x^{2} -x + 2x - 2 )=0 \\ \\ 2x^{2}(x-1)+2[x(x-1)+2(x-1)]=0 \\ \\ 2x^{2}(x-1)+2(x-1)(x+2)=0 \\ \\ (x-1)[2x^{2} +2(x+2)]=0 \\ \\ (x-1)(2x^{2} + 2x + 4)=0 \\ \\ 2(x-1)(x^{2} + x + 2) = 0 \\ \\ x-1=0 \ \vee \ x^{2}+x+2=0 \\ \\ \boxed{x=1} \\ \\ \Delta = 1^{2} - 4*1*2 \ \textless \ 0 \implies x\not\in R](https://tex.z-dn.net/?f=-2x%5E%7B3%7D-2x%2B4%3D0+%5C%5C++%5C%5C+2x%5E%7B3%7D+%2B+2x+-+4%3D0+%5C%5C++%5C%5C+2x%5E%7B3%7D++-+2x%5E%7B2%7D+%2B+2x%5E%7B2%7D+%2B+2x+-+4%3D0+%5C%5C++%5C%5C+2x%5E%7B2%7D%28x-1%29+%2B+2%28x%5E%7B2%7D+%2B+x+-2%29+%3D+0+%5C%5C++%5C%5C+2x%5E%7B2%7D%28x-1%29+%2B+2%28x%5E%7B2%7D+-x+%2B+2x+-+2+%29%3D0+%5C%5C++%5C%5C+2x%5E%7B2%7D%28x-1%29%2B2%5Bx%28x-1%29%2B2%28x-1%29%5D%3D0+%5C%5C++%5C%5C+2x%5E%7B2%7D%28x-1%29%2B2%28x-1%29%28x%2B2%29%3D0+%5C%5C++%5C%5C+%28x-1%29%5B2x%5E%7B2%7D+%2B2%28x%2B2%29%5D%3D0+%5C%5C++%5C%5C+%28x-1%29%282x%5E%7B2%7D+%2B+2x+%2B+4%29%3D0+%5C%5C++%5C%5C+2%28x-1%29%28x%5E%7B2%7D+%2B+x+%2B+2%29+%3D+0+%5C%5C++%5C%5C+x-1%3D0+%5C+%5Cvee+%5C+x%5E%7B2%7D%2Bx%2B2%3D0+%5C%5C++%5C%5C+%5Cboxed%7Bx%3D1%7D+%5C%5C++%5C%5C+%5CDelta+%3D+1%5E%7B2%7D+-+4%2A1%2A2+%5C+%5Ctextless+%5C++0+%5Cimplies+x%5Cnot%5Cin+R+ "-2x^{3}-2x+4=0 \\ \\ 2x^{3} + 2x - 4=0 \\ \\ 2x^{3} - 2x^{2} + 2x^{2} + 2x - 4=0 \\ \\ 2x^{2}(x-1) + 2(x^{2} + x -2) = 0 \\ \\ 2x^{2}(x-1) + 2(x^{2} -x + 2x - 2 )=0 \\ \\ 2x^{2}(x-1)+2[x(x-1)+2(x-1)]=0 \\ \\ 2x^{2}(x-1)+2(x-1)(x+2)=0 \\ \\ (x-1)[2x^{2} +2(x+2)]=0 \\ \\ (x-1)(2x^{2} + 2x + 4)=0 \\ \\ 2(x-1)(x^{2} + x + 2) = 0 \\ \\ x-1=0 \ \vee \ x^{2}+x+2=0 \\ \\ \boxed{x=1} \\ \\ \Delta = 1^{2} - 4*1*2 \ \textless \ 0 \implies x\not\in R")
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