Answer :
Answer:
The correct answer is B) y_x^3 , x^2_y^2 , xy^3.
To find the three geometric means (G.M.'s) between x4 and y4, we can use the formula:
G.M. = (x^n * y^n)^(1/n)
where n is the index (in this case, n = 4).
The three G.M.'s are:
1. (x^4 * y^0)^(1/4) = x^1 * y^0 = x
2. (x^3 * y^1)^(1/4) = x^3/4 * y^1/4 = x^3_y/4 = y_x^3
3. (x^2 * y^2)^(1/4) = x^2/4 * y^2/4 = x^1/2 * y^1/2 = x^2*y^2
4. (x^1 * y^3)^(1/4) = x^1/4 * y^3/4 = x^1/4 * y^3/4 = xy^3
5. (x^0 * y^4)^(1/4) = x^0 * y^1 = y
So, the three G.M.'s between x4 and y4 are y_x^3, x^2_y^2, and xy^3.