Question

решите систему уравнение х+у=5, х^3+у^3=35

Answer 1

x+Y=5⇒y=5-x
x³+y³=(x+y)(x²-xy+y²)=35
5(x²-xy+y²)=35
(x²-xy+y²)=35/5=7
x²-x(5-x)+(5-x)²-7=0
x²-5x+x²+25-10x+x²-7=0
3x²-15x+18=0
x²-5x+6=0
x1+x2=5 U x1*x2=6
x1=2⇒y1=5-2=3
x2=3⇒y2=5-3=2
(2;3) U (3;2)