if x^a=y^b=z^c and ab+bc+ca=0, then find xyz

• let x^a=y^b=z^c= K1(Constant)
  then a log x = b log y = c log z = log K1 = K (Constant)
  then log x = K/a, log y = K/b, log z = K/c
  
  Now, xyz = P (constant)
  log xyz = log P = log x + log y +log z = k/a + k/b + k/c = k (bc+ca+ab/abc)
  ab+bc+ca = 0 (given)
  So k (bc+ca+ab/abc) = k (0/abc) = k (0) = 0
  log P = 0
  P = 1 = xyz
• 7 years agoHelpfull: Yes(0) No(0)