a4+1/a4=119, then a3-1/a3=????

• ANSWER==>36
  a^4+1/a^4 = (a^2+1/a^2)^2 - 2*a^2*1/a^2 =119
  or (a^2+1/a^2)^2 -2 = 119
  or (a^2+1/a^2)^2 = 121
  hence a^2+1/a^2 = 11
  
  again (a-1/a)^2 +2*a*1/a = 11
  hence (a-1/a) = 3
  
  now a^3-1/a^3 = (a-1/a)(a^2+1/a^2+a*1/a) = 3*(11+1) = 3*12 = 36
• 10 years agoHelpfull: Yes(35) No(0)
• (a^2+1/a^2)^2=(a^4+1/a^4+2)
  hence a^2+1/a^2=11
  (a-1/a)^2=a^2+1/a^2-2
  a-1/a=3
  (a-1/a)^3=a^3-1/a^3-3(a-1/a)
  a3+1/a3=27+9=36
• 10 years agoHelpfull: Yes(4) No(0)
• @pronoy bej what about the(a-1/a)=-3???how can u ignore this value??
  
• 10 years agoHelpfull: Yes(1) No(1)
• a3-1/a3=(a-1/a)(a2 + 1+ 1/a2)........(1
  simplify the given equation
  (a2)^2 + (1/a2)^2+2*a2*1/a2=121
  (a2+1/a2)=11...........(2) hence a2+1/a2+1=11+1=12;
  a2+1/a2- 2*a*1/a=11-2
  (a-1/a)^2=9
  a-1/a=3......
  use these values in eq1
  3*12=36
• 10 years agoHelpfull: Yes(1) No(0)
• a^4+1/a^4=(a^2+1/a^2)^2-2.a.1/a=119
  =>a^2+1/a^2=+-11
  Both are square terms so we take only +11
  Now,(a^2+1/a^2)=11
  (a-1/a)^2+2.a.1/a=11
  (a-1/a)=+-3
  Now (a^3-1/a^3)
  =(a-1/a)(a^2+1+1/a^2)
  =+or-3 multiplied by 12
  = +/-36
• 10 years agoHelpfull: Yes(0) No(2)
• a4+1/a4=(a2 + 1/a2)^2 -2=119
  (a2 + 1/a2)^2=121=11
  (a - 1/a)^2-2=11
  (a - 1/a)=3;
  now a3-1/a3=(a-1/a)^3+3(a-1/a)=3^3+3*3=36
  
• 9 years agoHelpfull: Yes(0) No(0)