Correct Answer: a=16 & b=27.

Explanation:

a এবং b এর মান কত হলে (64x$^{3}$-9ax$^{3}$+108$^{3}$-b) একটি পুর্ণ ঘন হবে?

We know, (p-q)$^{3}$=p$^{3}$-3p$^{2}$q+3pq$^{2}$-q$^{3}$……..(i)

Now to make the term 64x$^{3}$-9ax$^{3}$+108$^{3}$-b into a perfect cube, we will equate all its term with the equation (i)

so, 1$^{st}$ term, p$^{3}$ = 64x$^{3}$=(4x)$^{3}$

=> p=4x

so,3$^{nd}$ term, 3pq$^{2}$ = 108x

=> $3\times 4\times q^{2}\times =3\times 4x\times 3^{2}$

=> q$^{2}$= 3$^{3}$ =>q=3

so, 2$^{nd}$ term , 3p$^{2}$q = 9ax$^{2}$

=> $9\times (4x)^{2}\times 3=9ax^{2}$

=> $9\times 16\times x^{2}=9ax^{2}$

so, a= 16

4$^{th}$ trem , q$^{3}$= b => 3$^{3}$= b

so, b =27