if a+(1)/a=1, then the value of a^3 is

• a+(1)/a=1,we can write
  (a+(1)/a)^3=1^3
  a^3+(1/a)^3+3=1
  a^3+(1/a)^3=-2
  a=-1
• 12 years agoHelpfull: Yes(6) No(4)
• Answer: 0.
  Explanation:
  a+1/a=1;
  a^2 +1 = a or a^2 - a +1 =0;
  now a^3=(1-1/a)^3=(1-1/a)(1 -1/a+1/a^2)=(1-1/a)((a^2 - a +1)/a) =0;
• 12 years agoHelpfull: Yes(3) No(7)
• if a+(1)/a=1,then
  a=1-1/a
  
  a^3=(1-1/a)^3
  so we can see (1-1/a)^3 as (a-b)^3
  (a-b)^3=a^3-b^3-3ab(a-b)
  a^3-b^3-3a^2b+3ab^2
  likeas
  
  (1-1/a)^3=(1)^3-(1/a)^3-3/a+3/a^2
  =1-1/a^3-3/a+3/a^2
  =(1-3/a)+(3/a^2-1/a^3)
  =1/a((1/a)-3)-1/a^2((1/a)-3)
  =((1/a)-3)(1/a-1/a^2)
  so from this we can find roots
  (1/a)-3=0
  3a-1=0 a=1/3
  
  (1/a)-(1/a^2)=0
  (a-1)/a^2=0
  a=1
  so value of a is 1, 1/3
  so value of a^3 can be 1,1/9(ans)
  
  
• 12 years agoHelpfull: Yes(2) No(2)
• a+1/a=1
  a^2-a+1=0
  solving,a=-(4+i(3)^0.5)/4 and .....
• 12 years agoHelpfull: Yes(0) No(1)