Question-26348

Question Number 26348 by RoachDN last updated on 24/Dec/17

Commented by RoachDN last updated on 24/Dec/17

short trick to solve ?

Answered by $@ty@m last updated on 24/Dec/17

\frac{x^{4} + \frac{1}{x^{4}} + 1}{x^{2} + \frac{1}{x^{2}} + 1} w h e r e x = \frac{6}{5}

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

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

= x^{2} + \frac{1}{x^{2}} - 1

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

= {(\frac{6}{5} - \frac{5}{6})}^{2} + 1

= {(\frac{36 - 25}{30})}^{2} + 1

= {(\frac{11}{30})}^{2} + 1

= \frac{121}{900} + 1

= \frac{1021}{900}

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