Salut,
256 = 2⁸.
Suma coeficienților binomiali este 2ⁿ = 2⁸, deci n = 8.
Termenul general al dezvoltării este:
[tex]T_{k+1}=C_n^k\cdot a^{n-k}\cdot b^k=C_{8}^k\cdot\left(x^{\frac{1}3}\right)^{8-k}\cdot\left(x^{-\frac{1}4}\right)^k=C_{8}^k\cdot x^{\frac{8-k}3-\frac{k}4};\\\\\dfrac{8-k}3-\dfrac{k}4=-\dfrac{1}4\Bigg|\cdot 12\Rightarrow 4(8-k)-3k=-3,\ deci\ 32-7k=-3,\ deci\ k=5.\\\\Termenul\ este\ deci\ T_6=C_{8}^5\cdot x^{-\frac{1}4}.[/tex]
Green eyes.
