作业帮问一道解二元二次方程组的题目
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/11/05 14:46:59
问一道解二元二次方程组的题目
x^2-2xy+3y^2=9
4x^2-5xy+6y^2=30
4x^2-8xy+12y^2=4(x^2-2xy+3y^2)=36
6y^2-3xy=(4x^2-8xy+12y^2)-(4x^2-5xy+6y^2)=6
2y^2-xy=(6y^2-3xy)/2=2
4y^2-2xy=2(2y^2-xy)=4
x^2-y^2=(x^2-2xy+3y^2)-(4y^2-2xy)=5
4x^2-8xy+12y^2=6(6y^2-3xy)=36
4x^2+10xy-24y^2=0
2x^2+5xy-12y^2=0
(x+4y)(2x-3y)=0
x=-4y或x=2/3y
代入x^2-y^2=5解得
x=-4根号3/3,y=根号3/3
4x^2-5xy+6y^2=30
4x^2-8xy+12y^2=4(x^2-2xy+3y^2)=36
6y^2-3xy=(4x^2-8xy+12y^2)-(4x^2-5xy+6y^2)=6
2y^2-xy=(6y^2-3xy)/2=2
4y^2-2xy=2(2y^2-xy)=4
x^2-y^2=(x^2-2xy+3y^2)-(4y^2-2xy)=5
4x^2-8xy+12y^2=6(6y^2-3xy)=36
4x^2+10xy-24y^2=0
2x^2+5xy-12y^2=0
(x+4y)(2x-3y)=0
x=-4y或x=2/3y
代入x^2-y^2=5解得
x=-4根号3/3,y=根号3/3