对于x,y,若x-1的绝对值≤1,y-2的绝对值≤1,则x-2y+1的绝对值的最大值是5解法是|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5:|x-1|=1且|y-1|=1,且x-10得x=0,y=3等号成立问|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2
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![对于x,y,若x-1的绝对值≤1,y-2的绝对值≤1,则x-2y+1的绝对值的最大值是5解法是|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5:|x-1|=1且|y-1|=1,且x-10得x=0,y=3等号成立问|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2](/uploads/image/z/8599022-62-2.jpg?t=%E5%AF%B9%E4%BA%8Ex%2Cy%2C%E8%8B%A5x-1%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E2%89%A41%2Cy-2%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E2%89%A41%2C%E5%88%99x-2y%2B1%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF5%E8%A7%A3%E6%B3%95%E6%98%AF%7Cx-2y%2B1%7C%3D%7C%28x-1%29-2%EF%BC%88y-2%29-2%29%7C%E2%89%A4%7Cx-1%7C%2B2%7Cy-1%7C%2B2%E2%89%A41%2B2%2B2%3D5%3A%7Cx-1%7C%3D1%E4%B8%94%7Cy-1%7C%3D1%2C%E4%B8%94x-10%E5%BE%97x%3D0%2Cy%3D3%E7%AD%89%E5%8F%B7%E6%88%90%E7%AB%8B%E9%97%AE%7Cx-2y%2B1%7C%3D%7C%28x-1%29-2%EF%BC%88y-2%29-2%29%7C%E2%89%A4%7Cx-1%7C%2B2%7Cy-1%7C%2B2)
对于x,y,若x-1的绝对值≤1,y-2的绝对值≤1,则x-2y+1的绝对值的最大值是5解法是|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5:|x-1|=1且|y-1|=1,且x-10得x=0,y=3等号成立问|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2
对于x,y,若x-1的绝对值≤1,y-2的绝对值≤1,则x-2y+1的绝对值的最大值是5
解法是|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5
:|x-1|=1且|y-1|=1,且x-1<0且y-2>0得x=0,y=3等号成立
问|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5
:|x-1|=1且|y-1|=1,且x-1>0且y-2<0可以么?
对于x,y,若x-1的绝对值≤1,y-2的绝对值≤1,则x-2y+1的绝对值的最大值是5解法是|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5:|x-1|=1且|y-1|=1,且x-10得x=0,y=3等号成立问|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2
|x-2y+1|=|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2≤1+2+2=5
|(x-1)-2(y-2)-2)|≤|x-1|+2|y-1|+2
这个式子等号成立的条件是
x-1 ;-2(y-2);-2这三个数的符号相同
第三个是-2,那么前2个都是负值时才能取等号
取补到等号求最值失败
∴ |x-1|=1且|y-1|=1,且x-1>0且y-2