已知x、y、z>0 有方程组{x²+xy+y² y²+yz+z² x²+xz+z² 求x+y+zx²+xy+y² =9 y²+yz+z² =4 x²+xz+z² =1
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![已知x、y、z>0 有方程组{x²+xy+y² y²+yz+z² x²+xz+z² 求x+y+zx²+xy+y² =9 y²+yz+z² =4 x²+xz+z² =1](/uploads/image/z/3180459-3-9.jpg?t=%E5%B7%B2%E7%9F%A5x%E3%80%81y%E3%80%81z%3E0+%E6%9C%89%E6%96%B9%E7%A8%8B%E7%BB%84%7Bx%26%23178%3B%2Bxy%2By%26%23178%3B+y%26%23178%3B%2Byz%2Bz%26%23178%3B+x%26%23178%3B%2Bxz%2Bz%26%23178%3B+%E6%B1%82x%2By%2Bzx%26%23178%3B%2Bxy%2By%26%23178%3B+%3D9+y%26%23178%3B%2Byz%2Bz%26%23178%3B+%3D4+x%26%23178%3B%2Bxz%2Bz%26%23178%3B+%3D1)
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已知x、y、z>0 有方程组{x²+xy+y² y²+yz+z² x²+xz+z² 求x+y+zx²+xy+y² =9 y²+yz+z² =4 x²+xz+z² =1
已知x、y、z>0 有方程组{x²+xy+y² y²+yz+z² x²+xz+z² 求x+y+z
x²+xy+y² =9 y²+yz+z² =4 x²+xz+z² =1
已知x、y、z>0 有方程组{x²+xy+y² y²+yz+z² x²+xz+z² 求x+y+zx²+xy+y² =9 y²+yz+z² =4 x²+xz+z² =1
题目有点问题吧……
是不是等于3呢??
谢谢你们的提醒,上述解答需要修正。最终结果是:无解。 ---- 回复 adgeafc:你说得完全正确。我漏了最后一步,应当再验证一下,从而得出z<0的矛盾,由此说明题目无解。前面的“连续函数2012-8-20 14:54 没错!y²+yz+z² =4 x²+xz+z² =1看出y≤2,x≤1;明显x²+xy+y² ≤7 ” 说得也很好,一下子看出题目有问题。都很强。