已知x大于0,y大于0,且1/x+9/y=1,求x+y的最小值x+y=(x+y)*1=(x+y)*(1/x+9/y)=1+9+y/x+9x/y=10+y/x+9x/y 因为x,y∈(0,+∞) 运用基本不等式 这步怎么运用基本不等式呢 x+y=10+y/x+9x/y>=2√9+10=16 当且仅当y/x=9x/yy^2=9x^2
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![已知x大于0,y大于0,且1/x+9/y=1,求x+y的最小值x+y=(x+y)*1=(x+y)*(1/x+9/y)=1+9+y/x+9x/y=10+y/x+9x/y 因为x,y∈(0,+∞) 运用基本不等式 这步怎么运用基本不等式呢 x+y=10+y/x+9x/y>=2√9+10=16 当且仅当y/x=9x/yy^2=9x^2](/uploads/image/z/378237-21-7.jpg?t=%E5%B7%B2%E7%9F%A5x%E5%A4%A7%E4%BA%8E0%2Cy%E5%A4%A7%E4%BA%8E0%2C%E4%B8%941%2Fx%2B9%2Fy%3D1%2C%E6%B1%82x%2By%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BCx%2By%3D%28x%2By%29%2A1%3D%28x%2By%29%2A%281%2Fx%2B9%2Fy%29%3D1%2B9%2By%2Fx%2B9x%2Fy%3D10%2By%2Fx%2B9x%2Fy+%E5%9B%A0%E4%B8%BAx%2Cy%E2%88%88%280%2C%2B%E2%88%9E%29+%E8%BF%90%E7%94%A8%E5%9F%BA%E6%9C%AC%E4%B8%8D%E7%AD%89%E5%BC%8F+%E8%BF%99%E6%AD%A5%E6%80%8E%E4%B9%88%E8%BF%90%E7%94%A8%E5%9F%BA%E6%9C%AC%E4%B8%8D%E7%AD%89%E5%BC%8F%E5%91%A2+x%2By%3D10%2By%2Fx%2B9x%2Fy%EF%BC%9E%EF%BC%9D2%E2%88%9A9%2B10%3D16+%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93y%2Fx%3D9x%2Fyy%5E2%3D9x%5E2)
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