`pq+qr -pr -r^(2)`

If q is the mean proportional between p and r , show that : pqr (p + q + r)^(3) = (pq + qr + pr)^(3) .

if p,q,r be real then the interval in which f(x) =|underset(pr" "qr" "x+r^(2))underset(pq" "x+q^(2)" "qr)(x+p^(2)" "pq" "pr)|,

Simplify (pq - qr) ^(2) + 4 pq ^(2) r

Simplify the following:(pq-qr+ pr) (pq+qr)-(pr+pq) (p+q-r).

Prove that |{:(p^(2)+1,pq,pr),(pq,q^(2)+1,qr),(pr,qr,r^(2)+1):}|=1+p^(2)+q^(2)+r^(2)

If p, q, r be real then the intervals in which, f(x)=|(x+q^(2),pq,pr),(pq,x+p^(2),qr),(pr,qr,x+r^(2))|

If p, q, r be real, then the intervals in which, f(x)=|(x+p^2,pq,pr),(pq,x+q^2,qr),(pr,qr,x+r^2)|

Find the product of the following. (p^2+4q^2+r^2+2pq+pr-2qr) (p-2q-r)

If p = 4, q= 3 and r = -2, find the values of : (p^(2)+q^(2)-r^(2))/(pq+qr-pr)