if the geometric mean of two numbers x and y is 6 find the geometric mean of the four numbers x,y,9x,9y
"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
Well, to find the geometric mean of four numbers, you first need to find the product of all four numbers and then take the fourth root of that product. In this case, since the geometric mean of x and y is 6, we can conclude that xy = 36.
Now, with the four numbers being x, y, 9x, and 9y, we can find their product.
(x)(y)(9x)(9y) = 81(xy)(xy) = 81(36)(36) = 104976.
Finally, we take the fourth root of 104976, which is approximately 19. So, the geometric mean of the four numbers x, y, 9x, and 9y is...ta-da...19!
To find the geometric mean of the four numbers x, y, 9x, and 9y, we need to multiply them all together and then take the fourth root of the result.
Step 1: Multiply the four numbers together.
Product = x * y * 9x * 9y
Step 2: Simplify the product.
Product = 81 * x^2 * y^2
Step 3: Take the fourth root of the product.
Geometric Mean = ∛(81 * x^2 * y^2)
Since we know that the geometric mean of x and y is 6, we can substitute this information into the equation:
6 = √(x * y)
Squaring both sides of the equation, we have:
36 = x * y
Substituting this simplified equation into Step 3, we get:
Geometric Mean = ∛(81 * 36 * x^2 * y^2)
Geometric Mean = ∛(2916 * x^2 * y^2)
Therefore, the geometric mean of the four numbers x, y, 9x, and 9y is ∛(2916 * x^2 * y^2).
To find the geometric mean of four numbers x, y, 9x, and 9y, we can use the formula for the geometric mean:
Geometric Mean = √(Product of the numbers)
Step 1: Find the product of the four numbers.
Product = x * y * 9x * 9y
Step 2: Simplify the expression.
Product = 81 * x^2 * y^2
Step 3: Find the square root of the product.
Geometric Mean = √(81 * x^2 * y^2)
Step 4: Simplify the expression.
Geometric Mean = 9 * x * y
So, the geometric mean of the four numbers x, y, 9x, and 9y is 9xy.