已知x>0,y>0,x+2y+2xy=8,求x+2y的最小值.x+2y+2xy=8≥2倍根号下2xy+2xy 令根号下xy=t,t≥0,则2t的平
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![已知x>0,y>0,x+2y+2xy=8,求x+2y的最小值.x+2y+2xy=8≥2倍根号下2xy+2xy 令根号下xy=t,t≥0,则2t的平](/uploads/image/z/1662859-19-9.jpg?t=%E5%B7%B2%E7%9F%A5x%3E0%2Cy%3E0%2Cx%2B2y%2B2xy%3D8%2C%E6%B1%82x%2B2y%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC.x%2B2y%2B2xy%3D8%E2%89%A52%E5%80%8D%E6%A0%B9%E5%8F%B7%E4%B8%8B2xy%2B2xy+%E4%BB%A4%E6%A0%B9%E5%8F%B7%E4%B8%8Bxy%3Dt%2Ct%E2%89%A50%2C%E5%88%992t%E7%9A%84%E5%B9%B3)
已知x>0,y>0,x+2y+2xy=8,求x+2y的最小值.x+2y+2xy=8≥2倍根号下2xy+2xy 令根号下xy=t,t≥0,则2t的平
已知x>0,y>0,x+2y+2xy=8,求x+2y的最小值.x+2y+2xy=8≥2倍根号下2xy+2xy 令根号下xy=t,t≥0,则2t的平
已知x>0,y>0,x+2y+2xy=8,求x+2y的最小值.x+2y+2xy=8≥2倍根号下2xy+2xy 令根号下xy=t,t≥0,则2t的平
设xy=t,t≥0,
2√(2t)+2t-8≤0
2√(2t)≤8-2t
两边都大于0,分别平方,8-2t≥0,t≤4
8t≤64-32t+4t²
解得t≤2或t≥8
因为8-2t≥0,t≤4
所以0≤t≤2
x+2y=8-2t
x+2y的最小值为4