Let p, q and r be three distinct positive real numbers. If D= | array lll p & q & r q & r & p r & p & q array | , then which one of the following is correct?

Step-by-step solution

aligned D & = | array lll p & q & r q & r & p r & p & q array | & =p (r q-p^2 )+q (p r-q^2 )+r (p q-r^2 ) & =3 p q r-p^3-q^3-r^3 & =- (p^3+q^3+r^3-3 p q r ) aligned For real and distinct positive real value of p, q and r . aligned & p^3+q^3+r^3-3 p q r 0 & D 0 . aligned