Question

Se considera dezvoltarea (2 \sqrt{x} + \frac{3}{x} )^{6},x>0. Determinati termenul independent de x.

Answer 1

[tex]T_{k+1}=C_6^k*(2\sqrt{x})^{6-k}*(\frac{3}{x})^k\\ T_{k+1}=C_6^k*2^{6-k}*3^k*x^{\frac{6-k}{2}-k}\\ \frac{6-k}{2}-k=0 =\ \textgreater \ 6-k-2k=0=\ \textgreater \ k=2\\ T_3=C_6^2*2^4*3^2=\frac{6!}{2!*4!}*16*9=15*16*9=2160[/tex]