Question

p+q+r-=0,then what is value of p2/qr+q2/pr+r2/pq=?

Answer 1

As per question
             p+q+r=0
⇒          p+q= -r
⇒         (p+q)³= (-r)³
⇒          p³+q³+3p²q+3pq²= -r³
⇒          p³+q³+r³ = -3pq(p+q)
⇒          p³+q³+r³=3pqr
⇒         (p³+q³+r³)/pqr=3
⇒          p²/qr+q²/pr+r²/pq = 3

Answer 2

p+q+r=0
p+q=-r
 cubing on both sides
 (p+q)3=(-r)3
 p3+q3+3p2q+3pq2=-r3
p3+q3+r3=3pqr
(p3+q3+r3)/pqr=3
p2/qr+q2/pr+r2/pq=3