Q If a+1/a=1 then a3=?

• Given a+1/a=1
  multiply with a^2 both sides
  a^3+a=a^2_______(1)
  =>a(a^2+1)=a^2
  =>a^2=a-1;
  now from 1, a^3=a^2-1=>a^3+a=a-1=>a^3=-1
  
• 9 years agoHelpfull: Yes(23) No(8)
• a+1/a=1,
  a^2+1=a;
  a^2-a+1=0;
  (a+1)(a^2-a+1)=(a+1)*0;
  a^3+1=0;
  a^3=-1;
  
• 9 years agoHelpfull: Yes(17) No(0)
• Since a+1/a=1, we can 1/a=1-a ---- assume equation (1)
  Now, taking square on both side
  we get
  a^2 + 1/a^2 + 2=1
  a^2 + 1/a^2 = -1 put the value of 1/a form equation (1)
  a^2 + (1-a)^2=-1
  a^2 + 1 + a^2 -2*a=-1
  2*a^2 - 2*a=-2
  a^2 - a =-1
  a(a-1)=-1
  a=-1,0
  Here a=0 mean, there is no meaning
  so, finally a=-1
  and Answer is: a^3=-1
  
  
  
• 9 years agoHelpfull: Yes(13) No(9)
• a+1/a=1
  a^2+1=a => a^2=a-1
  a^2-a+1=0
  multiplying and devide by a
  a^3-a^2+a=0
  a^3=a^2-a
  a^3=a-1-a
  a^3=-1
• 9 years agoHelpfull: Yes(4) No(3)
• (a+1)/a=1
  (a+1)^2=a^2
  a^2+2a+1=a^2
  2a=-1
  a=-1/2
  a^3=-1/8 ans
• 9 years agoHelpfull: Yes(3) No(7)
• (a+1/a)=1
  multiplying both side by (a-1/a)
  (a+1/a)(a-1/a)=(a-1/a)
  a^2-1/a^2=a-1/a
  a^2-a=1/a^2-1/a
  a(a-1)=1/a^2(1-a)
  a^3(a-1)=(-1)(a-1)
  a^3= -1
• 6 years agoHelpfull: Yes(2) No(0)
• it's undetermined.......
• 9 years agoHelpfull: Yes(1) No(5)
• a+1/a=1
  => a^2 +1=a
  => a^2=a-1 .......(1)
  => a^3=a^2-a
  => a^3=a-1-a
  => a^3= - 1 .....ans
  
• 8 years agoHelpfull: Yes(0) No(1)
• given that
  a+(1/a)=1 multiply by a^2 on both sides then
  a^3+a=a^2 ...............1
  a(a^2+1)=a^2
  a^2+1=a
  a^2=a-1
  from eq 1
  a^3+a=a^2
  a^3=a^2-a
  a^3=a-1-a
  a^3=-1
  
• 8 years agoHelpfull: Yes(0) No(2)