若x,y,z>0且满足x²+xy+y²=49,y²+yx+z²=36,z²+xz+x²=25,求x+y+z的值
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![若x,y,z>0且满足x²+xy+y²=49,y²+yx+z²=36,z²+xz+x²=25,求x+y+z的值](/uploads/image/z/1638107-35-7.jpg?t=%E8%8B%A5x%2Cy%2Cz%3E0%E4%B8%94%E6%BB%A1%E8%B6%B3x%26%23178%3B%2Bxy%2By%26%23178%3B%3D49%2Cy%26%23178%3B%2Byx%2Bz%26%23178%3B%3D36%2Cz%26%23178%3B%2Bxz%2Bx%26%23178%3B%3D25%2C%E6%B1%82x%2By%2Bz%E7%9A%84%E5%80%BC)
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若x,y,z>0且满足x²+xy+y²=49,y²+yx+z²=36,z²+xz+x²=25,求x+y+z的值
若x,y,z>0且满足x²+xy+y²=49,y²+yx+z²=36,z²+xz+x²=25,求x+y+z的值
若x,y,z>0且满足x²+xy+y²=49,y²+yx+z²=36,z²+xz+x²=25,求x+y+z的值
题好像不太对啊,第二个式子貌似不对.初中生?给的49,36,25,我觉得应该是X^2+2xy+Y^2=49,这样的话(x+y)^2=49,x+y=7,同理y+z=6,x+z=5,三个式子相加得2( +y+z)=5+6+7,得x+y+z=9 要真是题里面的式子,那就真不会了,想了十五分钟也没想出来.个人拙见.
y²+yx+z²=36 yx应该是yz
x²+xy+y²=49 (x+y)的完全平方=49 所以x+y=7
y²+yz+z²=36,(y+z)的完全平方=36所以y+z=6
同理z+x=5
所以x+y+y+z+z+x=18
所以x+y+z=9