Question-146606

Question Number 146606 by iloveisrael last updated on 14/Jul/21

Answered by som(math1967) last updated on 14/Jul/21

x + \sqrt{x^{2} - 1} + \frac{1}{x - \sqrt{x^{2} - 1}} = 20

\frac{x^{2} - x^{2} + 1 + 1}{x - \sqrt{x^{2} - 1}} = 20

\frac{1}{x - \sqrt{x^{2} - 1}} = 10

x - \sqrt{x^{2} - 1} = \frac{1}{10}

a g a i n \frac{1}{x - \sqrt{x^{2} - 1}} = 10

\frac{x + \sqrt{x^{2} - 1}}{x^{2} - x^{2} + 1} = 10

x + \sqrt{x^{2} - 1} = 10

∴ 2 x = 10 + \frac{1}{10} = \frac{101}{10}

x = \frac{101}{20}

n o w x^{2} + \sqrt{x^{4} - 1} + \frac{1}{x^{2} + \sqrt{x^{4} - 1}}

x^{2} + \sqrt{x^{4} - 1} + \frac{x^{2} - \sqrt{x^{4} - 1}}{x^{4} - x^{4} + 1}

= 2 x^{2} = 2 \times {(\frac{101}{20})}^{2}