Prove that there is no term involving x^6 in the expansion of (2x^2 - 3/x )^11 ​

Question

Prove that there is no term involving x⁶ in the expansion of (2x² - \(\frac{3}x\))¹¹

Answer 1

To Prove: that there is no term involving x⁶ in the expansion of (2x² - \(\frac{3}x\))¹¹

Formula Used: General term, T_r+1 of binomial expansion (x + y)ⁿ is given by,

Now, finding the general term of the expression, (2x² - \(\frac{3}x\))¹¹, we get

For finding the term which has x⁶ in it, is given by 

22 – 2 r – r = 6 

3r = 16 

r = 16/3

Since,  r = 16/3 is not possible as r needs to be a whole number

Thus, there is no term involving x⁶ in the expansion of (2x² - \(\frac{3}x\))¹¹