Question 773286
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find three numbers in geometric progression whose sum is 19 and product is 216.
Ans:
Let the middle term be x and the common ratio be r. Then the 1st and 3rd terms are
x/r and x*r respectively.
Product = (x/r)*x*r*x = x^3 = 216.
So middle term x = 6.
Then the sum of the 3 terms = 6/r + 6 + 6*r = 19.
{{{6/r + 6*r - 13 = 0}}}
Multiplying by r
{{{6*r^2 - 13*r + 6 = 0}}} This is a standard quadratic equation which can be
solved using the quadratic solver, as shown below.
The 2 roots are r = 2/3 and r = 3/2.
Hence the other 2 terms of the GP are (6*2/3) and (6/(2/3) = 4 and 9.
The 3 numbers are 4,6 and 9 (or 9,6 and 4).
Hope you got it :)
Solution using quadratic solver: *[invoke quadratic "x", 6, -13, 6 ]
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