Question

termenul din dezvoltarea binomului (√x supra 2 +∛x² supra 2)la puterea 12 care contine x la puterea 6

Answer 1

$T_{k+1}= C_{12} ^{k} * (x^{ \frac{1}{2} }) ^{12-k}* ( x^{ \frac{2}{3} }) ^{k}$
$(\frac{1}{2})*(12-k)+( \frac{2}{3} )k= x^{6}$
$\frac{12-k}{2}+ \frac{2k}{3}=6$
$\frac{36-3k+4k}{6}=6$
36+k=36
k=0
deci $T_{1}$ il contine pe $x^{6}$
$T_{1}=12* x^{6}* x^{1}=12x^6$