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Radical Minimization Mission (Posted on 2025-01-09)

Find the minimum value of

(√(x²+4) + √(x²+7√(3)x + 49))²

No Solution Yet Submitted by Danish Ahmed Khan

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Calculus solution

Comment 1 of 1

https://www.desmos.com/calculator/8gf6moazl7

I used Desmos to work through the algebra.

The outer square can be ignored at first since the function is always positive:

g(x)=√(x²+4) + √(x²+7√(3)x + 49)

Then take the derivative (eq 4), set to zero (eq 5) and solve.

The minimum occurs when

x=-14sqrt(3)/11

Then evaluate

f(-14sqrt(3)/11) = 67

Posted by Jer on 2025-01-10 12:48:53

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