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Question

If x+1x=a,x2+1x3=b, then x3+1x2 is
  1. a3+a23a2b
  2. a3a23a+4b
  3. a3a2+3a6b
  4. a3+a2+3a16b

A
a3a23a+4b
B
a3+a2+3a16b
C
a3+a23a2b
D
a3a2+3a6b
Solution
Verified by Toppr

x+1x=a,x2+1x3=b(x+1x)2=a2x2+1x2+2=a2.....(i)(x+1x)3=a3x3+1x3+3(x+1x)=a3....(ii)

Adding equation (i) and (i)

x3+1x3+3(x+1x)+x2+1x2+2=a2+a3x2+1x3+x3+1x2+3(x+1x)+2=a2+a3b+x3+1x2+3a+2=a2+a3x3+1x2=a2+a33ab2

So option A is correct

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