If m^2+m^-2=23;then what is the value of m^3+m^-3?

• m^2+m^-2=23
  => (m + m^-1)^2 - 2 = 23
  => (m + m^-1) = 5
  
  m^3+m^-3 = (m + m^-1)^3 - 3(m + m^-1) = 5^3 - 3*5 = 110
• 10 years agoHelpfull: Yes(18) No(1)
• Ans:110
  
  m^2+(1/m^2)=23
  
  m+1/m=?
  
  By solving. (m+1/m)^2 =m^2 + 1/m^2 + 2
  
  We get m + 1/m = 5
  
  Use a^3+b^3 formula by keeping a=m, b=1/m
  
  m^3+1/m^3=(m+1/m)(m^2-m(1/m)+1/m^2)
  
  =5 (23-1)
  
  =110.
• 10 years agoHelpfull: Yes(5) No(0)
• here m2+m-2=23 can be written as m2+1/m2=23
  (it can be also written as in the format of (a+b)2=a2+b2=2ab))
  m2+1/m2+2(m)(1/m)=m2+1/m2+2=(m+1/m)2
  so (m+1/m)2=23+2(because m2+1/m2=23)
  m+1/m=5
  (a3+b3=(a+b)(a2-ab+b2))
  m^3+1/m^3=(m+1/m)(m^2-m(1/m)+1/m^2)
  
  =5 (23-1)
  
  =110.
  
  
  
  
• 10 years agoHelpfull: Yes(2) No(0)