Relationship Between A.M. and G.M.

If H.M. of two number is 4 , then A.M. 'A' and G.M. 'G' satisfy the relation 2A + G^(2) = 27 , then modulus of difference of these two numbers is

If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G.M. between aa n dbw h i l eq , q ' are , respectively, the A.M. and G.M. between ba n dc , then p^2+q^2=p^('2)+q^('2) b. p q=p ' q ' c. p^2-q^2=p^('2)-q^('2) d. none of these

Let two numbers have A.M.=9 and G.M.=4 Then these numbers are the roots of the quadratic equation

If the ratio of A.M. and G.M. of two positive numbers a and b is m : n, then prove that : a:b=(m+sqrt(m^(2)-n^(2))):(m-sqrt(m^(2)-n^(2)))

Sum and product of slopes of two lines through the origin are respectively the A.M. And G.M. of 9 and 16. Joint equation of bisectors of these lines is

If both the A.M. between m and n and G.M. between two distinct positive numbers a and b are equal to (ma+nb)/(m+n) , then n is equal to