Решить систему {х+у=5 {х^3+у^3=35 буду

35 = x^3 + y^3 = (x+y)*(x^2 - xy + y^2) = W,
т.к. x+y=5, то y=5-x, и
W = 5*(x^2 - xy +y^2) = 5*(x^2 - x*(5-x) + (5-x)^2 ) = 5*( x^2 - 5x +x^2 + 25 -10x + x^2) = 5*( 3*x^2 - 15x + 25) = 35,
3*x^2 - 15x + 25 = 35/5 = 7;
3*x^2 - 15x + 25 - 7=0;
3*x^2 - 15x + 18 =0;
x^2 - 5x + 6 = 0;
D = 5^2 - 4*6 = 25 - 24 = 1;
x1 = (5-1)/2 = 4/2 = 2;
x2 = (5+1)/2 = 6/2 = 3;
1) x1 = 2, тогда y1 = 5-x = 5-2 = 3;
2) x2 = 3, тогда y2 = 5-x = 5-3 = 2.
ответ. (2;3), (3;2).