解方程:(x-1)(x²+x+1)-x(x+3)=8求方程x²-y²=11的整数值
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解方程:(x-1)(x²+x+1)-x(x+3)=8求方程x²-y²=11的整数值
解方程:(x-1)(x²+x+1)-x(x+3)=8
求方程x²-y²=11的整数值
解方程:(x-1)(x²+x+1)-x(x+3)=8求方程x²-y²=11的整数值
因式分解
(x-y)(x+y) = 11
x-y=1
x+y=11
或者x,y互换.x=6,y=5或者 x=5,y=6
(x-1)(x²+x+1)-x(x+3)-8=
x^3-3x-x^2-9=(x^3-3x-6x)-(x^2+9-6x)=
x(x+3)(x-3)-(x-3)^2=
[x(x+3)-(x-3)](x-3)=
(x^2+2x+3)(x-3)=0
因2^2-4*1*3=-10<0,故,x=3
x²-y²=(x+y)(x-y)=11*1,
故分类
1>x+y=11,x-y=1,得x=6,y=5
2>x+y=1,x-y=11,得x=6,y=-5