Задачи

[Гост]

Решете уравнението
x/2 × (x-((1-×)/2))= ((-x+1)^2 - 1)/2

[ammornil]

Решете уравнението
x/2 × (x-((1-×)/2))= ((-x+1)^2 - 1)/2

[tex]\\ \text{ДМ: } \forall{x}\in\mathbb{R} \\ \frac{x}{2}\cdot{}\left(x-\frac{1-x}{2} \right)=\frac{(-x+1)^{2}-1}{2} \quad |\cdot{}2\ne{0} \\ x\cdot{}\underbrace{\left(x-\frac{1-x}{2} \right)}_{2}=(1-x)^{2}-1 \\ \quad \\ x\cdot{}\frac{2x-1+x}{2}=1^{2}-2\cdot{1}\cdot{x}+x^{2}-1 \\ \quad \\ \underbrace{x\cdot{}\frac{3x-1}{2}=x^{2}-2x}_{2} \\ \quad \\ x\cdot{}(3x-1)=2\cdot{}(x^{2}-2x) \\ 3x^{2}-x=2x^{2}-4x \\ x^{2}+3x=0 \\ x\cdot{}(x+3)=0 \\ x_{1}=0 \quad \cup \quad x_{2}=-3[/tex]