If the term independent of x in the expansion | vedclass

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(B) The general term $T_{r+1}$ in the expansion of $(x^{\frac{2}{3}} + \alpha x^{-3})^{22}$ is given by:$T_{r+1} = {}^{22}C_r \cdot (x^{\frac{2}{3}})^

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$1$

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(B) The general term $T_{r+1}$ in the expansion of $(x^{\frac{2}{3}} + \alpha x^{-3})^{22}$ is given by:$T_{r+1} = {}^{22}C_r \cdot (x^{\frac{2}{3}})^{22-r} \cdot (\alpha x^{-3})^r$$T_{r+1} = {}^{22}C_r \cdot \alpha^r \cdot x^{\frac{44-2r}{3} - 3r}$For the term to be independent of $x$,the exponent of $x$ must be $0$:$\frac{44-2r}{3} - 3r = 0$$44 - 2r - 9r = 0$$11r = 44 \implies r = 4$Given that the independent term is $7315$:${}^{22}C_4 \cdot \alpha^4 = 7315$$\frac{22 	imes 21 	imes 20 	imes 19}{4 	imes 3 	imes 2 	imes 1} \cdot \alpha^4 = 7315$$7315 \cdot \alpha^4 = 7315$$\alpha^4 = 1 \implies |\alpha| = 1$

If the term independent of $x$ in the expansion of $\left( x^{\frac{2}{3}} + \frac{\alpha}{x^3} \right)^{22}$ is $7315$,then $|\alpha|$ is equal to $...........$.

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