jacks said:My Solution:
Given \(\displaystyle \displaystyle \sqrt{x^4-9x^2-12x+61}-\sqrt{x^4-x^2+1} = \sqrt{\left(x^2-5\right)^2+\left(x-6\right)^2}-\sqrt{\left(x^2-1\right)^2+(x-0)^2}\)
Now Using Triangle Inequality::
\(\displaystyle \displaystyle \sqrt{\left(x^2-5\right)^2+\left(x-6\right)^2}-\sqrt{\left(x^2-1\right)^2+(x-0)^2}\leq \sqrt{\left(x^2-5-x^2+1\right)^2+\left(x-6-x\right)^2} = 2\sqrt{13}\)
and equality hold when \(\displaystyle \displaystyle \frac{x^2-5}{x-6} = \frac{x^2-1}{x}\)
The Optimization Challenge II is a scientific competition designed to find the best solution to a given problem through the use of mathematical and computational methods.
The winner of the Optimization Challenge II is determined by evaluating the performance of submitted solutions against a set of pre-determined criteria. The solution with the highest score will be declared the winner.
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