Đáp án:
`M={43}/6`
Giải thích các bước giải:
`\qquad a;b;c\ge 0`
`\qquad a+ab+b=3`
`=> (ab+b)+a+1=3+1`
`=>b(a+1)+a+1=4`
`=>(a+1)(b+1)=4` $(1)$
$\\$
`\qquad b+bc+c=8`
`=>(bc+c)+b+1=8+1`
`=>c(b+1)+b+1=9`
`=>(b+1)(c+1)=9` $(2)$
$\\$
`\qquad c+ca+a=15`
`=>(ca+a)+c+1=15+1`
`=>a(c+1)+c+1=16`
`=>(c+1)(a+1)=16` $(3)$
Vì `16\ne 0=>c+1\ne 0; a+1\ne 0`
`=>a+1={16}/{c+1}` thay vào `(1)`
`(1)=>{16}/{c+1}.(b+1)=4`
`=>4(c+1)=16(b+1)`
`=>c+1=4(b+1)` thay vào `(2)`
`(2)=>(b+1).4(b+1)=9`
`=>(b+1)^2=9/4`
`=>`$\left[\begin{array}{l}b+1=\dfrac{3}{2}\\b+1=\dfrac{-3}{2}\end{array}\right.$`=>`$\left[\begin{array}{l}b=\dfrac{1}{2}\\b=\dfrac{-5}{2}\ (loại)\end{array}\right.$
Với `b=1/2`
`\qquad c+1=4(b+1)`
`=>c+1=4.(1/2+1)=4. 3/2=6`
`=>c=5` (thỏa mãn)
$\\$
`\qquad a+1={16}/{c+1}={16}/{5+1}={16}/6=8/3`
`=>a=8/3-1=5/3` (thỏa mãn)
$\\$
`M=a+b+c=5/3+1/2+5={13}/6+5={43}/6`
Vậy `M={43}/6`
