求f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}的最小值用max{a,b,c}表示a,b,c三个数中的最大值,设f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}(x,y∈R
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![求f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}的最小值用max{a,b,c}表示a,b,c三个数中的最大值,设f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}(x,y∈R](/uploads/image/z/3769706-2-6.jpg?t=%E6%B1%82f%28x%2Cy%29%3D%2Cmax%7B%7C%EF%BC%88x-y%EF%BC%89%2F%EF%BC%88x%2B2y%2B3%EF%BC%89%7C%2C%EF%BC%88x%2B2%EF%BC%89%2F%EF%BC%88x%2B2y%2B3%EF%BC%89%2C%EF%BC%885y%2B4%EF%BC%89%2F%EF%BC%88x%2B2y%2B3%EF%BC%89%7D%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E7%94%A8max%EF%BD%9Ba%2Cb%2Cc%EF%BD%9D%E8%A1%A8%E7%A4%BAa%2Cb%2Cc%E4%B8%89%E4%B8%AA%E6%95%B0%E4%B8%AD%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%2C%E8%AE%BEf%28x%2Cy%29%3D%2Cmax%7B%7C%EF%BC%88x-y%EF%BC%89%2F%EF%BC%88x%2B2y%2B3%EF%BC%89%7C%2C%EF%BC%88x%2B2%EF%BC%89%2F%EF%BC%88x%2B2y%2B3%EF%BC%89%2C%EF%BC%885y%2B4%EF%BC%89%2F%EF%BC%88x%2B2y%2B3%EF%BC%89%7D%EF%BC%88x%2Cy%E2%88%88R)
求f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}的最小值用max{a,b,c}表示a,b,c三个数中的最大值,设f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}(x,y∈R
求f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}的最小值
用max{a,b,c}表示a,b,c三个数中的最大值,设f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}(x,y∈R),求f(x,y)的最小值
求f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}的最小值用max{a,b,c}表示a,b,c三个数中的最大值,设f(x,y)=,max{|(x-y)/(x+2y+3)|,(x+2)/(x+2y+3),(5y+4)/(x+2y+3)}(x,y∈R
令(x-y)/(x+2y+3)> 0 ,有(x-y)/(x+2y+3)+(x+2)/(x+2y+3)+(5y+4)/(x+2y+3)=2 ,f(x,y)的最小值为2/3(x=-8,y=-2).若(x-y)/(x+2y+3)〈 0,设(x-y)〈0,则(x+2y+3)> 0,y〉x,令y=x+t,有t>0,(y-x)/(x+2y+3)+(x+2)/(x+2y+3)+(5y+4)/(x+2y+3)=2+2t/(3x+2t+3)>2,f(x,y)的最小值大于2/3.设y0,(y-x)/(x+2y+3)+(x+2)/(x+2y+3)+(5y+4)/(x+2y+3)=2-2s/(3y+s+3)>2,f(x,y)的最小值大于2/3.所以f(x,y)的最小值为2/3(x=-8,y=-2).
f(x,y)≥|(x-y)/(x+2y+3)|≥(x-y)/(x+2y+3)
f(x,y)≥(x-y)/(x+2y+3)……1
f(x,y)≥(x+2)/(x+2y+3)……2
f(x,y)≥(5y+4)/(x+2y+3)……3
1+2+3得
3f(x,y)≥(x-y+x+2+5y+4)/(x+2y+3)=(2x+4y+6)/(x+2y+3)=2
f...
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f(x,y)≥|(x-y)/(x+2y+3)|≥(x-y)/(x+2y+3)
f(x,y)≥(x-y)/(x+2y+3)……1
f(x,y)≥(x+2)/(x+2y+3)……2
f(x,y)≥(5y+4)/(x+2y+3)……3
1+2+3得
3f(x,y)≥(x-y+x+2+5y+4)/(x+2y+3)=(2x+4y+6)/(x+2y+3)=2
f(x,y)≥2/3
当x-y=x+2=5y-4成立
x=-8
y=-2检验成立
f(x,y)min=2/3
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