CM:$\forall n\geqslant 5,n\subset N* thì 3^{n}>n\times2^{n}+3\times n^{2}(1) $*n=5$\rightarrow (1) đúng$
*giả sử (1) đúng với n=k$\rightarrow 3^{k}>k\times 2^{k}+3\times k^{2}(2)$
*CM:$3^{k+1}>(k+1)\times 2^{k+1}+3\times (k+1)^{2}\Leftrightarrow 3^{k+1}>2\times (k+1)\times 2^{k}+3\times k^{2}+6k+3(3)$
(2)$\rightarrow 3^{k+1}>3\times (k\times 2^{k}+3\times k^{2})\rightarrow VT(3)-VP(3)>(k-2)2^{k}-6k-3$
mặt khác k$\geqslant 5\rightarrow VT(3)-VP(3)>26k-67>0$
$\rightarrow ĐPCM$