Show that `((4m)/3-(3n)/4)^2 +2mn`=`16/9m^2+9/16 n^2`

Show that S_(n)=(n(2n^(2)+9n+13))/(24) .

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

If cosec theta- sin theta = m and sec theta - cos theta = n , prove that: (m^(2)n)^(2/3)+(n^(2)m)^(2/3)=1 .

Simplify (m^2-n^2m)^2+ 2m^3n^2

Show that 3^(n) xx 4^(m) cannot end with the digit 0 or 5 for any natural numbers ‘n’and 'm'

Simplify (4m+5n)^2+(5m+4n)^2

If m is the A.M. of two distinct real numbers l and n""(""l ,""n"">""1) and G1, G2 and G3 are three geometric means between l and n, then G1 4+2G2 4+G3 4 equals, (1) 4l^2 mn (2) 4l^m^2 mn (3) 4l m n^2 (4) 4l^2m^2n^2

Subtract: -m^2+5mn from 4m^2-3mn+8

The ratio of the sums of m and n terms of an A.P is m^(2):n^(2) . Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) .

Compute (3m -2n) ^(3)