[tex]a;b;c\epsilon \left [ 0;1 \right ]\rightarrow \left\{\begin{matrix} b^{2}\leq b;c^{3}\leq c & \\ abc\geq 0 & \end{matrix}\right.[/tex]
[tex]\rightarrow VT\leq a+b+c-ab-bc-ca\left ( 1 \right )[/tex]
[tex]gt\rightarrow \left ( a-1 \right )\left ( b-1 \right )\left ( c-1 \right )\leq 0\Leftrightarrow a+b+c-ab-bc-ca+abc-1\leq 0\Leftrightarrow a+b+c-ab-bc-ca\leq 1-abc\leq 1\left ( 2 \right )(do: abc\geq 0)[/tex]
Từ (1) và (2)=>đpcm