If 1/x+x=5 and find out the value x^5+1/x^5=?

• x + 1/x = 5
  
  first calculate (x + (1/x))^2
  (x + (1/x))^2 = 5^2
  x^2 + (1/x)^2 + 2 = 25
  x^2 + 1/x^2 = 23 ---->(1)
  
  
  Now calculate (x + (1/x))^3
  (x + 1/x)^3 = 5^3
  x^3 + y^3 +3x*1/x(x + 1/x) = 125
  x^3 + y^3 + 15 = 125
  x^3 + y^3 = 110 --->(2)
  
  Multiply (1) & (2)
  (x^2 + 1/x^2)(x^3 + 1/x^3) = 23 * 110
  x^5 + 1/x + x + 1/x^5 = 2530
  x^5 + 1/x^5 + 5 = 2350
  x^5 + 1/x^5 = 2345
  
  Ans : 2345
• 10 years agoHelpfull: Yes(6) No(3)
• I think that ans is 2525..... the procedure is right but when subtracting 2530 by 5 we get 2525..............
• 10 years agoHelpfull: Yes(4) No(0)
• Ya @Ahalya ... Its 2525...
• 10 years agoHelpfull: Yes(1) No(0)
• ans=100001
  1/2x=5
  10x=1
  x=1/10
  [x^5(1+1/x^5)]/x^5=1+100000=100001
  
• 10 years agoHelpfull: Yes(0) No(4)
• x^2 + 1/x^2 = (x+ 1/x)^2 - 2 = 5^2 - 2 = 23 -------(1)
  
  x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)
  
  multiplying (1)& (2)
  
  =>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110
  => x^5 + 1/x + x + 1/x^5 = 2530
  => x^5 + 1/x^5 + (x+ 1/x)= 2530
  => x^5 + 1/x^5 + 5 = 2530
  => (x^5+ 1/x^5)= 2345
  
• 10 years agoHelpfull: Yes(0) No(3)