$x - \frac{1}{x} = 4$ 4 হলে, প্রমাণ করুন যে, $x^{4} + \frac{1}{x^{4}} = 322 .$

Created: 1 year ago | Updated: 1 year ago

Updated: 1 year ago

দেওয়া আছে, $x - \frac{1}{x} = 4$

বামপক্ষ $= x^{4} + \frac{1}{x^{4}}$

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

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

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

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

= ( 4² + 2 )² - 2

= ( 16 + 2 )² - 2

= ( 18 )² - 2

= 324 - 2

= ডানপক্ষ

অতএব, $x^{4} + \frac{1}{x^{4}} = 322$ (প্রমাণিত)

1 year ago

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