Đáp án+Giải thích các bước giải:

`1) C = - \sqrt{x - 7/3} - |y - 8/3| + 10/3` (ĐKXĐ: `x >= 7/3`)

Do `-\sqrt{x - 7/3} <= 0 ∀ x >= 7/3`

`- | y - 8/3| <= 0 ∀ y \in RR`

`-> C <= 0 + 0 + 10/3 = 10/3`

Dấu "`=`" xảy ra khi `{(\sqrt{x - 7/3} = 0),(|y - 8/3| = 0):}`

`-> {(x - 7/3 = 0),(y - 8/3 = 0):}`

`-> {(x = 7/3),(y = 8/3):}`

Vậy `C_max = 10/3` khi `x = 7/3 ; y = 8/3`

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`2) C = 1/10 - | (x - 3)/5 |^3 - (y - 1/6)^2`

Do  `- | (x - 3)/5|^3 <= 0 ∀ x \in RR`

` - (y - 1/6)^2 <= 0 ∀ y \in RR`

`-> C <= 1/10 + 0 + 0 = 1/10`

Dấu "`=`" xảy ra khi `{( |(x - 3)/5| = 0),((y - 1/6)^2 = 0):}`

`-> {(x - 3 = 0),(y - 1/6 = 0):}`

`-> {(x = 3),(y = 1/6):}`

Vậy `C_max = 1/10` khi `x = 3 ; y = 1/6`

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`3) C = 1/3 - ( (3x)/2 - 1)^2 - 1/4|x - y|`

Do ` - ( (3x)/2 - 1)^2 <= 0 ∀ x \in RR`

`-1/4 |x - y| <= 0 ∀ x ;  y \in RR`

`-> C <= 1/3 + 0 + 0 = 1/3`

Dấu "`=`" xảy ra khi `{( ((3x)/2 - 1)^2 = 0),(|x - y| = 0):}`

`-> {( (3x)/2 - 1 = 0),(x - y = 0):}`

`-> {(x = 2/3),(y = x):}`

`-> x = y = 2/3`

Vậy `C_max = 1/3` khi `x = y = 2/3`

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`4) C = 1 + 4/(|x - 1| + 5)`

Do `|x - 1| + 5 >= 0 ∀ x \in RR`

`-> 4/(|x - 1| + 5) <= 4/5`

`-> C <= 1 + 4/5 = 9/5`

Dấu "`=`" xảy ra khi `|x - 1| = 0`

`-> x - 1 = 0`

`-> x = 1`

Vậy `C_max = 9/5` khi `x = 1`

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`5) C = 10 - 2/(|x + 1| + (y + 2)^2 + 5)`

Do `|x + 1|  >= 0 ∀ x \in RR`

`(y + 2)^2 >= 0 ∀ y \in RR`

`-> |x + 1| + (y + 2)^2 + 5 >= 0 + 0 + 5 = 5`

`-> 2/(|x+1| + (y + 2)^2 + 5) <= 2/5`

`-> - 2/(|x+1| + (y + 2)^2 + 5) >= -2/5`

`-> C >= 10 - 2/5 = 48/5`

Dấu "`=`" xảy ra khi `{(|x + 1| = 0),( (y + 2)^2 = 0):}`

`-> {(x + 1 = 0),(y + 2 = 0):}`

`-> {(x = -1),(y = -2):}`

Vậy `C_min = 48/5` khi `x = -1 ; y = -2`