CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If T0,T1,T2,Tn represent the terms in the expansion of (x+a)n, then the value of (T0T2+T4T6+)2+(T1T3+T5)2 is
  1. (a2x2)n
  2. (x2+a2)n
  3. (x2a2)n
  4. (x2+a2)2n


Solution

The correct option is B (x2+a2)n
(x+a)n=xn+C1xn1a+C2xn2a2+C3xn3a3+          (1)
=T0+T1+T2+T3+
=(T0+T2+T4+)+(T1+T3+T5)
The first bracket involves even powers of a and 2nd bracket involves odd powers of a. Also i2=1,i4=1,i3=i,i5=i Replacing a by ai and -ai respectively in (1), we get
(x+ai)n=(T0T2+T4)+i(T1T3+T5)            .... (i)
(xai)n=(T0T2+T4)i(T1T3+T5)             ....(ii)
Multiply (i) & (ii)
(x2+a2)n=(T0T2+T4)2+(T1T3+T5)2

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image