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Let \(a,\)  \(b,\) \(c,\) and \(d\) be positive real numbers such that \(36a + 4b + 4c + 3d = 25.\) Find the maximum value of \(a \times \sqrt{b} \times \sqrt[3]{c} \times \sqrt[4]{d}.\)

 Apr 9, 2019

Best Answer 

 #1
avatar+6196 
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\(\text{This one I'd do using Lagrange multipliers}\\ f(a,b,c,d) = a \cdot \sqrt{b} \cdot \sqrt[3]{c} \cdot \sqrt[4]{d}\\ g(a,b,c,d) = 36a+4b+4c+3d-25\\ \text{Solve}\\ \nabla(f-\lambda g) = 0\)

 

.
 Apr 9, 2019
 #1
avatar+6196 
+2
Best Answer

\(\text{This one I'd do using Lagrange multipliers}\\ f(a,b,c,d) = a \cdot \sqrt{b} \cdot \sqrt[3]{c} \cdot \sqrt[4]{d}\\ g(a,b,c,d) = 36a+4b+4c+3d-25\\ \text{Solve}\\ \nabla(f-\lambda g) = 0\)

 

Rom Apr 9, 2019

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