Question 1066281
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Find 3 numbers in the {{{highlight(cross(geometrical))}}} geometric progression whose sum is 28 and whose product is 512
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<pre>
Let the middle term be "x" and the common ratio be r.

Then the first of the three terms is {{{x/r}}}, and the third term is {{{x*r}}}.


The product of the three terms is {{{(x/r)*x*(xr)}}} = {{{x^3}}}.

Thus {{{x^3}}} = 512, which implies x = 8.

So, you just found the middle term. It is 8.


Then the sum of the three terms is {{{8/r + 8 + 8r}}} = 28, which gives you an equation

{{{8/r + 8r}}} = 28 - 8,   or  {{{8/r + 8r}}} = 28 - 8 = 20,   or   {{{1/r + r}}} = {{{20/8}}},   or  {{{1/r + r}}} = {{{5/2}}} = 2.5

which has the roots  r = 2  and/or  r= {{{1/2}}}.


Thus the progression is  {4, 8, 16}   or   {16, 8, 4}.
</pre>

Solved.