Question

Si x+$\frac{1}{x}$ = 7. Hallar $x^{2}$+$\frac{1}{x^{2}}$

Answer 1

Respuesta:

$Si \: \\ x+\frac{1}{x} = 7. \\ Hallar \\ x^{2}+\frac{1}{x^{2}} \\ \\ x + \frac{1}{x} = 7 \: despjamos \: x \\ \\ \frac{ {x}^{2} + 1 }{x} = 7 \\ {x }^{2} + 1 = 7x \\ x = \sqrt{7x + 1}$

${x}^{2} + \frac{1}{x^{2} } \\ \\ (\sqrt{7x + 1})^{2} + \frac{1}{( \sqrt{7x + 1)^{2} } } \\ 7x + 1 + \frac{1}{7x + 1} \\ \\ \frac{(7x + 1)(7x + 1) + 1}{7x + 1} \\ \\ 7x + 1 + 1 \\ \\ = 7x + 2 \: resultado$