Răspuns:
B) 45a⁴
Explicație pas cu pas:
[tex]\Big(a+\dfrac{1}{a^2}\Big)^{10} = (a+a^{-2})^{10}\\ \\\\ T_{k+1} = C_{n}^k\cdot x^{n-k}\cdot y^k\\ \\T_{k+1} =C_{10}^{k}\cdot a^{10-k}\cdot a^{-2\cdot k}\\ \\ T_{k+1} = C_{10}^{k}\cdot a^{10-k-2k}\\ \\ T_{k+1} = C_{10}^k\cdot a^{10-3k}\\ \\ 10-3k =4 \Rightarrow 3k = 6 \Rightarrow k = 2 \\ \\ \Rightarrow T_{2+1} = C_{10}^2\cdot a^{4} \\\\ \Rightarrow T_{3} = \dfrac{10!}{2!\cdot 8!}\cdot a^4 \\ \\\\ \Rightarrow \boxed{T_3 = 45a^4}[/tex]
