Giải thích các bước giải:

`\sqrt{(5a+4)(5b+4)}\le\frac{(5a+4)+(5b+4)}{2}=\frac{5a+5b+8}{2}` `\sqrt{(5b+4)(5c+4)}\le\frac{(5b+4)+(5c+4)}{2}=\frac{5b+5c+8}{2}}` `sqrt{(5c+4)(5a+4)}\le\frac{(5c+4)+(5a+4)}{2}=\frac{5c+5a+8}{2}}` 

`{5a+4}+\sqrt{5b+4}+\sqrt{5c+4}\)^2 =5a+5b+5c+12+2\sqrt{(5a+4)(5b+4)}+2\sqrt{(5b+4)(5c+4)}+2\sqrt{(5c+4)(5a+4)}}`

`\text{(a+b+c)+12+(5a+5b+8)+(5b+5c+8)+(5c+5a+8) =10(a+b+c)+36 =10+36=46}``\text{\Rightarrow\sqrt{5a+4}+\sqrt{5b+4}+\sqrt{5c+4}\le\sqrt{46}<\sqrt{51}}`