Đáp án:
Giải thích các bước giải:
`x^3+(66/(9+2\sqrt{3}))^3+(66/(9+2\sqrt{3}))^3>=3\root{3}{x^3.(66/(9+2\sqrt{3}))^3.(66/(9+2\sqrt{3}))^3}`
`=>x^3+(66/(9+2\sqrt{3}))^3+(66/(9+2\sqrt{3}))^3>=3x(66/(9+2\sqrt{3}))^2`
`4[y^3+(33/(9+2\sqrt{3}))^3+(33/(9+2\sqrt{3}))^3]>=4.3\root{3}{y^3.(33/(9+2\sqrt{3}))^3.(33/(9+2\sqrt{3}))^3}`
`=>4[y^3+(33/(9+2\sqrt{3}))^3+(33/(9+2\sqrt{3}))^3]>=12y.(33/(9+2\sqrt{3}))^2`
`=>4[y^3+(33/(9+2\sqrt{3}))^3+(33/(9+2\sqrt{3}))^3]>=3y.(66/(9+2\sqrt{3}))^2`
`3[z^3+((66\sqrt{3}-44)/23)^3+((66\sqrt{3}-44)/23)^3]>=3.3\root{3}{z^3.((66\sqrt{3}-44)/23)^3.((66\sqrt{3}-44)/23)^3}`
`=>3[z^3+((66\sqrt{3}-44)/23)^3+((66\sqrt{3}-44)/23)^3]>=3z(66/(9+2\sqrt{3}))^2`
`=>x^3+(66/(9+2\sqrt{3}))^3+(66/(9+2\sqrt{3}))^3+4[y^3+(33/(9+2\sqrt{3}))^3+(33/(9+2\sqrt{3}))^3]+3[z^3+((66\sqrt{3}-44)/23)^3+((66\sqrt{3}-44)/23)^3]>=3x(66/(9+2\sqrt{3}))^2+3y(66/(9+2\sqrt{3}))^2+3z(66/(9+2\sqrt{3}))^2`
`=>x^3+4y^3+3z^3+2(66/(9+2\sqrt{3}))^3+8(33/(9+2\sqrt{3}))^3+6((66\sqrt{3}-44)/23)^3>=3(x+y+z)(66/(9+2\sqrt{3}))^2`
`=>x^3+4y^3+3z^3+2(66/(9+2\sqrt{3}))^3+8(33/(9+2\sqrt{3}))^3+6((66\sqrt{3}-44)/23)^3>=3(x+y+z)(66/(9+2\sqrt{3}))^2`
`=>x^3+4y^3+3z^3+2(66/(9+2\sqrt{3}))^3+8(33/(9+2\sqrt{3}))^3+6((66\sqrt{3}-44)/23)^3>=3.11.(66/(9+2\sqrt{3}))^2`
`=>x^3+4y^3+3z^3>=33(66/(9+2\sqrt{3}))^2-2(66/(9+2\sqrt{3}))^3-8(33/(9+2\sqrt{3}))^3-6((66\sqrt{3}-44)/23)^3`
Dấu `=` xảy ra
`<=>`$\begin{cases} x=\dfrac{66}{9+2\sqrt{3} } \\y=\dfrac{33}{9+2\sqrt{3} } \\z= \dfrac{66\sqrt{3}-44 }{23 } \end{cases}$
