Find (a^2 + b^2) if
a^3 - b^3 + ab = 35^2
a^3 - b^3 - 3ab = 1

Where a,b are positive integers

• Ans:) 613..
  a^3 - b^3 + ab = 35^2
  a^3 - b^3 - 3ab = 1
  by solving these two equations we can get ab = 306
  and a^3 - b^3 = 919
  Identity 1:
  a^3 - b^3 = (a-b)^3 +3ab(a-b)
  lets assume (a-b) = x and we got a^3 - b^3 = 919 and ab = 306
  den x^3 - 0.x^2 +3(306)(x) = 919
  by solving the equation one root is 1
  so a-b = 1
  Identity 2:
  a^3 - b^3 = (a-b)(a^2 + ab + b^2)
  919 = (1)(a^2 + 306 + b^2)
  919 - 306 = (a^2 + b^2)
  therefore (a^3 - b^3) = 613...
  enjoyyy....
• 11 years agoHelpfull: Yes(5) No(0)
• if a^3-b^3+ab=15^2
  and a^3-b^3-3ab=1
  then a=8 and b=7
  and ans of a^2+b^2=113
• 11 years agoHelpfull: Yes(0) No(2)