(r+1)th term in the expansion of (ax3+bx311)15 is
Tr+1=Cr15(ax3)15−r(bx1/31)r
⇒Tr+1=Cr15(a)15−r(x)45−310r(b1)r
For the coefficient of x15 in (ax3+bx1/31)15:
45−310r=15
⇒30=310r
⇒r=9
Coefficient of x15=C915a6b−9
(r+1)th term in the expansion of (ax1/3−bx31)15 is:
Tr+1=Cr15(ax1/3)15−r(−bx31)r
For the coefficient of x−15 in (ax1/3−bx31)15 is:
5−3r−3r=−15
⇒310r=20
⇒r=6
Coefficient of x−15 =C615a9×b−6
Hence,
C915a6b−9=C615a9×b−6
⇒b6a9=b9a6
⇒a3b3=1⇒ab=1