[" 14.If "a" be the "A" ."M" .of two numbers "b" and "c" and "],[qquad [G_(1),G_(2)" are the two GMs between them then "],[" prove that "G_(1)^(3)+G_(2)^(3)=2abc]]

If a is A.M. of two positive numbers b and c and two G.M's between b and c are G_(1) and G_(2) , prove that G_(1)^(3) + G_(2)^(3) = 2abc .

If a be one A.M and G_(1) and G_(2) be then geometric means between b and c then G_(1)^(3)+G_(2)^(3)=

If m is the AM of two distinct real numbers l and n (l,ngt1) and G_(1),G_(2)" and "G_(3) are three geometric means between l and n, then G_(1)^(4)+2G_(2)^(4)+G_(3)^(4) equals

If m is the AM of two distinct real numbers l and n (l,ngt1) and G_(1),G_(2)" and "G_(3) are three geometric means between l and n, then G_(1)^(4)+2G_(2)^(4)+G_(3)^(4) equals

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 A be the A.M. of two given numbers and g_1 and g_2 be two G.M.'s between them,then show that- 2A=(g_1^2)/(g_2)+(g_2^2)/g_1 .

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

If m is the A.M of two distinct real number l and n (l,n gt 1) and G_(1),G_(2) and G_(3) are three geometric means between l and n, then G_(1)^(4) + 2G_(2)^(4) + G_(3)^(4) equal :

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 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