Answer to Question #120665 in Algebra for Rashed Khan

Question

If, pq+qr+rp= 0 then, (p^2)/(p^2-qr)+ (q^2)/(q^2-rp)+( r^2)/(r^2-pq) =?

Answer 1

Question:

If, pq+qr+rp= 0 then, (p^2)/(p^2-qr)+ (q^2)/(q^2-rp)+( r^2)/(r^2-pq) =?

Solution:

1 - step: pq = -(qr + rp), qr = -(rp + qp), rp = -(pq + qr).

2 - step: p²/(p²+rp+qp)+q²/(q²+qp+qr)+r²/(r²+qr+rp).

3 - step: p/(p+r+q)+q/(q+p+r)+r/(r+q+p) = (r+q+p)/(r+q+p)=1

Answer: 1.