Question

Hey , Anyone can help to solve this question

If X is Real then Find the Maximum value of
$\sqrt{x - 3} + \sqrt{133 - x}$

Answer 1

If x∈R find the maximum value of

x4−3x2−6x+13−−−−−−−−−−−−−−−√−x4−x2+1−−−−−−−−−√

I tried this:

Let

y=x4−3x2−6x+13−−−−−−−−−−−−−−−√−x4−x2+1−−−−−−−−−√

For maxima dydx=0 and d2ydx2<0. However, the equation dydx=0 (after simplifying and clearing the square roots) came out to be a nine degree equation which gave me a nightmare! Moreover, simplifying the derivative was also a tedious task. I found this question in my book in the chapter on theory of equation. I can't think of an algebraic solution