if the geometric mean of two numbers x and y is 6 find the geometric mean of the four numbers x,y,9x,9y

Answer 1

"the geometric mean of two numbers x and y is 6"
---> (xy)^(1/2) = 6
xy = 36

goemetric mean of x,y,9x,9y
= ( (x)(y)(9x)(9y) )^(1/4)
= ( 81x^2 y^2 )^(1/4)
= (81 (xy)^2 )^(1/4)
= (81(1296))^(1/4)
= 3(6)
= 18