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Algebra? (Posted on 2019-02-16) Difficulty: 3 of 5
Find the minimum of √(58 - 42x) + √(149 - 140√(1 - x2)), where -1 <= x <= 1.

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution via Wolfram Alpha Comment 1 of 1
It was during the solving of this puzzle on Wolfram Alpha that I decided to subscribe to Wolfram Alpha Pro.

Wolfram Alpha gives the answer as sqrt(109), at x = 300/763 - 3*sqrt(4441)/763 or (300 - 3sqrt(4441))/763 ~= .131163191378042.

The derivative of the function given in the puzzle was found to be f'(x) = (70 x)/(sqrt(1 - x^2) sqrt(149 - 140 sqrt(1 - x^2))) - 21/sqrt(58 - 42 x), which has a zero at the above mentioned value of x.

This is from Wolfram's text version of the step-by-step solution. 

  Posted by Charlie on 2019-02-16 15:11:11
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