# Minimize beats Solve

Posted 1 month ago
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 This is the second step in solving a problem Reygan Dionisio posted on LinkedIn Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] During evaluation := Solve::nsmet: This system cannot be solved with the methods available to Solve. Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] // FullSimplify 1 + Sqrt[2] MaxValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] // FullSimplify 1 + Sqrt[2] 
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Posted 1 month ago
 Frank,The reason Solve fails is that you have more variables in the equations than you told Solve about. This works (by adding res to the list of variables): Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k, res}] as does this (let Solve figure out the variables): Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}] However, the minimize approach runs faster if you know that the minimum is the solution.Regards,Neil
 MinValue is 100 times faster than Solve In[6]:= AbsoluteTiming[ Solve[{res == b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k, res}] // FullSimplify] Out[6]= {84.9759, {{a -> 9^(ArcSinh[1]/Log[5/3]), b -> 15^(ArcSinh[1]/Log[5/3]), k -> ArcSinh[1]/Log[5/3], res -> 1 + Sqrt[2]}}} In[2]:= AbsoluteTiming[ MinValue[{ b/a, a == 9^k, b == 15^k, a + 2 b == 25^k, a > 0, b > 0}, {a, b, k}] // FullSimplify] Out[2]= {0.399868, 1 + Sqrt[2]} 
 PositiveReals puts a constraint on every variable. A notebooks is attached with code. Attachments: