insert two geometric means between 32 and 4
Answer (1)
Answer:To insert two geometric means between 32 and 4, we need to find two numbers, x and y, such that 32, x, y, 4 form a geometric sequence. In a geometric sequence, the ratio between consecutive terms is constant. Let's call this constant ratio r. Then we have: - x = 32r- y = xr = 32r^2- 4 = yr = 32r^3 From the last equation, we can solve for r: 4 = 32r^3r^3 = \frac{4}{32} = \frac{1}{8}r = \sqrt[3]{\frac{1}{8}} = \frac{1}{2} Now we can find x and y: - x = 32r = 32(\frac{1}{2}) = 16- y = 32r^2 = 32(\frac{1}{2})^2 = 32(\frac{1}{4}) = 8 Therefore, the two geometric means between 32 and 4 are \boxed{16} and \boxed{8}.
