Question

найдите корни уравнения:
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Answer 1

$\displaystyle\bf\\(x^{2} -2x+2)\cdot(x^{2} -2x+3)=6\\\\x^{2} -2x+2=m \ \ \ \Rightarrow \ \ \ x^{2} -2x+3=m+1\\\\m\cdot(m+1)-6=0\\\\m^{2} +m-6=0\\\\Teorema \ Vieta \ :\\\\m_{1} + m_{2} =-1\\\\m_{1} \cdot m_{2} =-6\\\\m_{1} =-3 \ \ ; \ \ m_{2} =2\\\\1)\\\\x^{2} -2x+2=-3\\\\x^{2} -2x+5=0\\\\D=(-2)^{2}-4\cdot 5=4-20=-16 < 0\\\\x\in \oslash\\\\2)\\\\x^{2} -2x+2=2\\\\x^{2} -2x=0\\\\x\cdot(x-2)=0x_{1} =0\\\\x-2=0 \ \ \Rightarrow \ \ x_{2} =2\\\\Otvet \ : \ 0 \ ; \ 2$