If x+1/2x=2, find the value of 8x^3+1/x^3

• x+1/2x=2
  So, 2x+1/x=4.
  Now, 8x^3+1/x^3
  = (2x)^3 + (1/x)^3
  = (2x+1/x)^3 - 3*2x*(1/x)*(2x+1/x)
  = 4^3 - 3*2*4
  = 40
• 12 years agoHelpfull: Yes(6) No(2)
• (x+1)/2x=2
  x+1=4x
  x=1/3
  now put this value of x in eq (8x^3+1)/x^3,we get
  (8(1/3)^3+1)/(1/3)^3
  =((8*1/27)+1)/(1/27)
  after solving we get (35*27)/27=35(ans)
• 12 years agoHelpfull: Yes(2) No(9)
• x+1/2x=2
  
  (2x²+1)/2x= 2
  
  (2x²+1)/x= 4
  
  (2x + 1/x)³ = 8x³ +1/x³ +3*2x*1/x(2x+1/x)
  
  substituting 64 = 8x³+1/x³ +3*2*4
  
  64 = 8x³ +1/x³ +24
  
  8x³ +1/x³ =64 -24 =40
• 12 years agoHelpfull: Yes(2) No(2)
• x+1=4x
  3x=1
  then,x=1/3.........
  so solution of the equation 8x^3+1/x^3 and by putting the value of X and ANSWER =539
  
  
  MR.J.P.
• 12 years agoHelpfull: Yes(1) No(1)
• 8x^3+1/x^3
  =1/8*(x^3-1/8x^3)
  =1/8*((x+1/x)^3-3*x*(1/2x)*(x+1/x))
  =1/8*(2^3-3*(1/2)*2)
  =1/8*(8-3)
  =5/8
• 12 years agoHelpfull: Yes(0) No(6)