Question

ofer 100 de puncte.rezolvati sistemul:x²+y²=2
x³+y³=x²y+xy²

Answer 1

[tex]x^3+y^3=x^2y+xy^2\\ x^3-x^2y+y^3-xy^2=0\\ x^2(x-y)+y^2(y-x)=(x-y)(x^2-y^2)=0\Rightarrow\\ (x-y)(x-y)(x+y)=0\Rightarrow x=y\text{ sau }x=-y\\ \text{In ambele cazuri }x^2=y^2\\ \text{Prima ecuatie se mai scrie: }\\ 2x^2=2\Rightarrow x^2=1\Rightarrow x=\pm1\\ S=\{(1,1),(-1,-1),(1,-1),(-1,1)\} [/tex]