Question

If the term without $x$ in the expansion of $\left(x^{\frac{2}{3}}+\frac{\alpha}{x^3}\right)^{22}$ is 7315 , then $|\alpha|$ is equal to ___

Answer 1

The correct answer is 1.
Tr+1​=22Cr​⋅(x32​)22−r⋅(α)r,x−3r
=22Cr​⋅x344​−32r​−3r(α)r
344​=311r​
r=4
22C4​⋅α4=7315
2422×21×20×19​⋅α4=7315
α=1