3x的平方加xy加y的平方等于15,3x的平方减去31xy加上5y的平方等于负45

Question

如题所述

Answer 1

1---3x^2+xy+y^2=15
9x^2+3xy+3y^2=45
(9x^2+3xy+3y^2)+(3x^2-31xy+5y^2) = 0 =4*(3x^2-7xy+2y^2)
3x^2-7xy+2y^2 =(3x-y)(x-2y)=0;
y=3x,或x=2y
y=3x → 3x^2+xy+y^2 = 3x^2+3x^2+9x^2=15x^2=15,x=±1,y=±3.
x=2y → 12y^2+2y^2+y^2 =15,y=±1;x=±2 .