If `(p-q)/(2)=3 and rp-rq=12`, then r=

Let p,q,r varepsilon R^(+) and 27pqr>=(p+q+r)^(3) and 3p+4q+5r=12 then p^(3)+q^(4)+r^(5) is equal to

ifp+q+r=1 and pq+qr+rp=-1 and pqr=-1 find value of p^(3)+q^(3)+r^(3)

If pq + qr + rp = 0 , then what is the value of (p^(2))/(p^(2) - qr) + (q^(2))/(q^(2) - rp) + (r^(2))/(r^(2) - pq) ?

In Fig. two tangents RQ and RP are drawn from an external point R to the circle with centre O. If anglePRQ = 120 ^@ , then prove that OR = PR + RQ .

two tangents RQ and RP are drawn from an external point R to the circle with centre O. If /_PRQ =120^@ , then prove that OR= PR+ RQ

If p+q=1, then show that sum_(r=0)^nr^2^nC_rp^rq^(n-r)=npq+n^2p^2

If p+q=1, then show that sum_(r=0)^n r^2^n C_rp^r q^(n-r)=n p q+n^2p^2dot

If p+q=1, then show that sum_(r=0)^n r^2^n C_rp^r q^(n-r)=n p q+n^2p^2dot

Given points P(2,3), Q(4, -2), and R(alpha,0) . Find the value of a if PR + RQ is minimum.