ct-2-1-ct-2-2-2-c-2-t-4-1-t-4-Find-t-f-c-

Question Number 201864 by ajfour last updated on 14/Dec/23

{({c t}^{2} - \frac{1}{{c t}^{2}} + \sqrt{2})}^{2} = c^{2} (t^{4} + \frac{1}{t^{4}})

F i n d t = f (c) .

Commented by Frix last updated on 14/Dec/23

This is equivalent to

{(t^{2})}^{3} - \frac{(t^{2})}{c^{2}} + \frac{\sqrt{2} (1 - c^{4})}{4 c^{3}} = 0

which can be solved (method depending

on the value of 27 c^{8} - 54 c^{4} - 5)

Commented by ajfour last updated on 14/Dec/23

T h a n k s, c^{4} = 1 - 2 \sqrt{2} p & p^{2} < \frac{4}{27}

S i r h o w w o u l d y o u d o t h i s :

x^{4} - 9 x^{2} + 6 x - 1 = 0

I f i g u e d o u t a n i c e w a y f o r s u c h

c^{2} = 4 b d h o l d i n g b i q u a d r a t i c s .

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