已知x,y属于正整数,且x+4y=1 求x/1+1/y的最小值 并且求出x y利用条件x+4y=1,得1/x+1/y=(x+4y)/x+(x+4y)/y=1+4y/x+x/y+4=4y/x+x/y+5≥2√[(4y/x)(x/y)]+5 ……基本不等式a+b≥2√(ab)=4+5=9当且仅当 4y/x=x/y时成立即x²=4
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![已知x,y属于正整数,且x+4y=1 求x/1+1/y的最小值 并且求出x y利用条件x+4y=1,得1/x+1/y=(x+4y)/x+(x+4y)/y=1+4y/x+x/y+4=4y/x+x/y+5≥2√[(4y/x)(x/y)]+5 ……基本不等式a+b≥2√(ab)=4+5=9当且仅当 4y/x=x/y时成立即x²=4](/uploads/image/z/4033350-54-0.jpg?t=%E5%B7%B2%E7%9F%A5x%2Cy%E5%B1%9E%E4%BA%8E%E6%AD%A3%E6%95%B4%E6%95%B0%2C%E4%B8%94x%2B4y%3D1+%E6%B1%82x%2F1%2B1%2Fy%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC+%E5%B9%B6%E4%B8%94%E6%B1%82%E5%87%BAx+y%E5%88%A9%E7%94%A8%E6%9D%A1%E4%BB%B6x%2B4y%3D1%2C%E5%BE%971%2Fx%2B1%2Fy%3D%28x%2B4y%29%2Fx%2B%28x%2B4y%29%2Fy%3D1%2B4y%2Fx%2Bx%2Fy%2B4%3D4y%2Fx%2Bx%2Fy%2B5%E2%89%A52%E2%88%9A%5B%284y%2Fx%29%28x%2Fy%29%5D%2B5+%E2%80%A6%E2%80%A6%E5%9F%BA%E6%9C%AC%E4%B8%8D%E7%AD%89%E5%BC%8Fa%2Bb%E2%89%A52%E2%88%9A%28ab%29%3D4%2B5%3D9%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93+4y%2Fx%3Dx%2Fy%E6%97%B6%E6%88%90%E7%AB%8B%E5%8D%B3x%26sup2%3B%3D4)
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