3.+已知+x^3+y^3=4xy+1,+则+y`=
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亲,你好!3.+已知+x^3+y^3=4xy+1,+则+y`的解题思路是:x³+y³+3xy=1(x+y)³-3x²y-3xy²+3xy-1=0[(x+y)³-1]-3xy(x+y-1)=0(x+y-1)[(x+y)²+(x+y)+1]-3xy(x+y-1)=0(x+y-1)[(x+y)²+(x+y)+1-3xy]=0(x+y-1)(x²-xy+y²+x+y+1)=0(x+y-1)[(1/2)(x²+2x+1)+(1/2)(y²+2y+1)+(1/2)(x²-2xy+y²)]=0(x+y-1)[(x+1)²+(y+1)²+(x-y)²]=0x+y-1=0或(x+1)²+(y+1)²+(x-y)²=0x+y-1=0 x+y=1(x+1)²+(y+1)²+(x-y)²=0,平方项恒非负,三非负项之和=0,三非负项均=0解得x=-1 y=-1x+y=(-1)+(-1)=-2综上,得x+y=1或x+y=-2如果我的解答对您有所帮助,还请给个赞,期待您的赞,您的举手之劳对我很重要,您的支持也是我进步的动力。最后再次祝您身体健康,心情愉快!
咨询记录 · 回答于2022-11-18
3.+已知+x^3+y^3=4xy+1,+则+y`=
亲,你好!3.+已知+x^3+y^3=4xy+1,+则+y`的解题思路是:x³+y³+3xy=1(x+y)³-3x²y-3xy²+3xy-1=0[(x+y)³-1]-3xy(x+y-1)=0(x+y-1)[(x+y)²+(x+y)+1]-3xy(x+y-1)=0(x+y-1)[(x+y)²+(x+y)+1-3xy]=0(x+y-1)(x²-xy+y²+x+y+1)=0(x+y-1)[(1/2)(x²+2x+1)+(1/2)(y²+2y+1)+(1/2)(x²-2xy+y²)]=0(x+y-1)[(x+1)²+(y+1)²+(x-y)²]=0x+y-1=0或(x+1)²+(y+1)²+(x-y)²=0x+y-1=0 x+y=1(x+1)²+(y+1)²+(x-y)²=0,平方项恒非负,三非负项之和=0,三非负项均=0解得x=-1 y=-1x+y=(-1)+(-1)=-2综上,得x+y=1或x+y=-2如果我的解答对您有所帮助,还请给个赞,期待您的赞,您的举手之劳对我很重要,您的支持也是我进步的动力。最后再次祝您身体健康,心情愉快!
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不用点我头像,我看到就会回
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f这边有什么数字吗【4】