((1)/(2)^(1)pq-(3)/(2)q)times(pq-q)

((1) / (2) pq- (3) / (2) q) xx (pq-q)

tan ^(-1)""(1)/(p+q)+tan ^(-1)""(q)/(p^(2)+pq+1)=cot^(-1)p

Given pq + qr + rp = 0 find (1)/(p^(2)-qr) + (1)/(q^(2) -rp) + (1)/(r^(2) - pq) = ?

A transversal cut the same branch of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 in P,P' and the anymptotes in Q.Q' ,the value of (PQ+PQ')-(P'Q'-P'Q)

show that (4pq+3q)^(2)-(4pq-3q)^(2)=48pq^(2)

If 2010 is a root of x^(2)(1 - pq) - x(p^(2) + q^(2)) - (1 + pq) = 0 and 2010 harmonic mean are inserted between p and q then the value of (h_(1) - h_(2010))/(pq(p - q)) is

If 2010 is a root of x^(2)(1 - pq) - x(p^(2) + q^(2)) - (1 + pq) = 0 and 2010 harmonic mean are inserted between p and q then the value of (h_(1) - h_(2010))/(pq(p - q)) is

A transvers axis cuts the same branch of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at P and P' and the asymptotes at Q and Q'. Prove that PQ=P'Q' and PQ'=P'Q.