Q-Max-x-gt-1-x-4-x-2-x-6-2x-3-1-

Question Number 174227 by mnjuly1970 last updated on 27/Jul/22

Q :

{M a x}_{\underset{x > 1}{}} (\frac{x^{4} - x^{2}}{x^{6} + 2 x^{3} - 1}) = ?

Commented by infinityaction last updated on 27/Jul/22

\frac{1}{6} ? ? ?

Commented by mnjuly1970 last updated on 27/Jul/22

y e s S i r \dots

Commented by infinityaction last updated on 27/Jul/22

p = \frac{x - \frac{1}{x}}{x^{3} - \frac{1}{x^{3}} + 2} = \frac{x - \frac{1}{x}}{(x - \frac{1}{x}) (x^{2} + \frac{1}{x^{2}} + 1) + 2}

p = \frac{x - \frac{1}{x}}{(x - \frac{1}{x}) {{(x - \frac{1}{x})}^{2} + 3} + 2}

l e t x - \frac{1}{x} = g

p = \frac{g}{g (g^{2} + 3) + 2} \Rightarrow \frac{1}{g^{2} + \frac{2}{g} + 3}

p = \frac{1}{g^{2} + \frac{1}{g} + \frac{1}{g} + 3}

p_{m a x} = \frac{1}{3 + 3} = \frac{1}{6}

Commented by mnjuly1970 last updated on 27/Jul/22

v e r y n i c e s o l u t i o n

t h a n k s a l o t s i r