(ct^2 −(1/(ct^2 ))+(√2))^2 =c^2 (t^4 +(1/t^4 )) Find t=f(c).


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
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

$T h a n k s, c^{4} = 1 - 2 \sqrt{2} p & p^{2} < \frac{4}{27}$ $S i r h o w w o u l d y o u d o t h i s :$ $x^{4} - 9 x^{2} + 6 x - 1 = 0$ $I f i g u e d o u t a n i c e w a y f o r s u c h$ $c^{2} = 4 b d h o l d i n g b i q u a d r a t i c s .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum