If `G` is the geometric mean of `xa n dy` then prove that `1/(G^2-x^2)+1/(G^2-y^2)=1/(G^2)`

If G be the GM between x and y, then the value of (1)/(G^(2) - x^(2)) + (1)/(G^(2) - y^(2)) is equal to

If a is the A.M.of b and c and the two geometric mean are G_(1) and G_(2), then prove that G_(1)^(3)+G_(2)^(3)=2ab

If G be the GM between x and y, then the value of (1)/(G^(2)-x^(2))+(1)/(G^(2)-y^(2)) is equal to (A)G^(2)(B)(2)/(G^(2))(C)(1)/(G^(2))(D)3G^(2)

If G be the GM between x and y,then the value of (1)/(G^(2)-x^(2))+(1)/(G^(2)-y^(2)) is equal to

If a is the A.M.of b and c and the two geometric means are G_(1) and G_(2), then prove that G_(1)^(3)+G_(2)^(3)=2abc.

If g is the inverse of f and f'(x)=(1)/(1+x^(n)) prove that g'(x)=1+(g(x))^(n)

The geometric mean of the observation x_(1),x_(2),x_(3),……..,_(n) is G_(1) , The geometric mean of the observation y_(1),y_(2),y_(3),…..y_(n) is G_(2) . The geometric mean of observations (x_(1))/(y_(1)),(x_(2))/(y_(2)),(x_(3))/(y_(3)),……(x_(n))/(y_(n)) us

If a ,a_1, a_2, a_3, a_(2n),b are in A.P. and a ,g_1,g_2,g_3, ,g_(2n),b . are in G.P. and h s the H.M. of aa n db , then prove that (a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h