If (x+(1/x))=4,the value of (x5+(1/x5)) is:

A. 724 B. 500 C. 752 D. 525

• Assuming the question as (x + 1/x) = 4------(A)
  Squaring on both the sides we get
  x2 +(1/x2) + 2 = 16
  ⇒ x2 +(1/x2) = 14--------(B)
  Now
  (x2 +(1/x2))(x + 1/x)=14*4;
  (x3+1/x3) + (x + 1/x)=56;
  (x3+1/x3) = 56-(x + 1/x) ..... and we (x + 1/x) = 4
  Therefore .... (x3+1/x3) = 52------(C)
  
  Multiplying (B) and (C)...we get
  (x5+1/x5) + (x+1/x) = 14*52
  After solving we get....
  (x5+1/x5) = 724.
• 6 years agoHelpfull: Yes(20) No(0)
• (x^5+1/x^5)+4=(x^2+1/x^2) (x^3+1/x^3)
  now,x^2+1/x^2=(x+1/x)^2 -2 (using a^2+b^2+2ab=(a+b)^2)
  =>x^2+1/x^2=4^2-2=14
  and
  x^3-1/x^3=(x+1/x)(x^2-1+1/x^2)
  =>x^3+1/x^3=4 (14-1)=>4*13
  putting this in main equation we get,
  x^5+1/x^5=(14 * 4 *13)-4=>724
• 6 years agoHelpfull: Yes(2) No(0)