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Sagot :
Answer:
4, 8, 16.
Step-by-step explanation:
Let the three numbers in GP be [tex]r, ra, ra^2[/tex], where [tex]a \ne 0[/tex]. We are given that [tex]r + ra + ra^2 = 28[/tex] and [tex]r \cdot ra \cdot ra^2 = r^3a^3 = 512[/tex], the latter of which gives [tex]ra = \sqrt[3]{512} = 8[/tex]. So substituting this into the former equation gives [tex]\frac{8}{a} + 8 + 8a = 28[/tex] or
[tex]8 + 8a + 8a^2 = 28a\\2a^2 + 2a + 2 = 7a\\2a^2 - 5a + 2 = 0\\(2a-1)(a-2) = 0\\a = \frac{1}{2} \vee a = 2[/tex]
And this gives our answer directly.
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