If m^2 + m^-2=23
then find
m^3 + m^-3

• a^3+b^3=(a+b)(a^2+b^2-ab)
  here a=m,b=1/m;
  (m+1/m)(23-1);
  and (m+1/m)=(m2+1/m2+2)^1/2=5;
  =5*22=110
• 10 years agoHelpfull: Yes(10) No(1)
• 110.
  sqauring m+1/m we get the value of m+1/m.
  cubing m+1/m we get the required value
• 9 years agoHelpfull: Yes(3) No(1)
• (m+1/m)^2= m^2+1/m^2+2
  m^2+1/m^2=23
  m+1/m=5
  then
  make use of in m^3+m^-3
  so answer is 110
• 7 years agoHelpfull: Yes(3) No(0)
• 0 because 3m-3m=0 whatever may be value of m
• 7 years agoHelpfull: Yes(2) No(5)
• answer is 110
  solution is:-
  (m + (1/m))^2=m^2 + (1/m)^2 + 2*m*(1/m)
  (m + (1/m))^2=23 + 2*m*(1/m)=23+2=25
  so, (m + (1/m))=sqrt (25)=5
  
  now,
  (m + (1/m))^3=m^3 + (1/m)^3 + 3*m^2*(1/m) + 3*m*(1/m)^2
  5^3 - 3*m^2*(1/m) - 3*m*(1/m)^2 =m^3 + (1/m)^3
  5^3 - 3*(m +(1/m)) =m^3 + (1/m)^3
  5^3 - 3*5 = m^3 + (1/m)^3
  125-15=m^3 + (1/m)^3
  
  therefore, m^3 + (1/m)^3=110
• 7 years agoHelpfull: Yes(1) No(0)
• from (a+b)^2 formula,we can find (m+1/m).From (a+b)^3,we can find the solution. Answer is 110
• 7 years agoHelpfull: Yes(1) No(0)
• m^2+m^-2=23 ==> m+m^-1=5
  m^3+m^-3=(m+m^-1)^3-3(m+m^-1) = 125-3(5) = 125-15 = 110
• 7 years agoHelpfull: Yes(0) No(0)
• 110 and -110
• 7 years agoHelpfull: Yes(0) No(0)