.if p+q+r=0 then p^2/qr+q^2/pr+r^2/pq=?

• ans is 3!
  we know the relation if p+Q+R =0 then P3+q3+r3 = 3pqr
  here we can also write the given problem in the form: (p^3+q^3+r^3)/pqr = 3pqr/pqr= 3. ans
• 11 years agoHelpfull: Yes(16) No(11)
• answer is zero let us have the lcm we have p^3+q^3+r^3/p*q*r since we have a^3+b^3+c^3=(a+b+c)(......) since given p+q+r=0 ans is zero
• 11 years agoHelpfull: Yes(11) No(4)
• 3 is answer
• 11 years agoHelpfull: Yes(2) No(0)
• wheather any relationship between p,q & r
  in case we consider p=1 q=2 r=-3
  p^2/qr+q^2/pr+r^2/pq= 15/6
  ie the case and ans will depend upon the condition or option
• 11 years agoHelpfull: Yes(1) No(5)
• p3+q3+r3/pqr==>(p+q+r)(2pq+2qr+2rp)/pqr==>0
• 9 years agoHelpfull: Yes(1) No(0)
• as simplyfying p2/qr+q2/pr+r2/pq we get
  (p3+q3+r3)/pqr
  as a3+b3+c3=(a+b+c) (a2+b2+c2-ab-bc-ca)+3abc
  we know a+b+c=0
  hence a3+b3+c3=3abc
  ie; 3pqr/pqr=3
  ans is 3
• 7 years agoHelpfull: Yes(1) No(0)
• let us assume q+r be s then do cube
  (p+s)^3=p^3+s^3+3p^2s+3ps^2
  substitute assumption s equation
  
  (p+q+r)^3= p^3 + (q+r)^3 + 3p^2(q+r) +3p(q+r)^2
  
  In the question they give p+q+r=0
  
  0=p^3 + q^3+r^3 +(3q^2r +3r^2q+3p^2r+3p^2q+3pq^2+3pr^2+6pqr)
  
  inside braces equation get common 3pqr
  0=p^3+q^3+r^3+3pqr{2(p+q+r)+2 }
  
  again apply p+q+r=0
  
  0=p^3+q^3+r^3+3pqr(2)
  -6pqr=p^3+q^3+r^3
  
  -6=p^2/qr+q^2/pr+r^2/pq
  
  
  therefore -6 is the answer
• 6 years agoHelpfull: Yes(0) No(0)