Question

解方程组x^2-y^2=5(x+y) x^2+xy+y^2=43

大家帮一下忙 谢谢了

Answer 1

x^2-y^2=5(x+y)
===> (x+y)(x-y)-5(x+y)=0
===> (x+y)(x-y-5)=0
===> x=-y，或者x=y+5
①当x=-y时，带入第二个有：x^2-x^2+x^2=43
===> x^2=43
===> x=±√43
则，y=±√43
②当x=y+5时，带入第二个有：(y+5)^2+(y+5)*y+y^2=43
===> y^2+10y+25+y^2+5y+y^2=43
===> 3y^2+15y-18=0
===> y^2+5y-6=0
===> (y-1)(y+6)=0
===> y=1，或者y=-6
所以，x=6，或者x=-1
综上：
①x=√43，y=-√43
②x=-√43，y=√43
③x=6，y=-1
④x=-6，y=1