Question

Se a + $\frac{1}{a}$ = 2,então a⁴ + $\frac{1}{a⁴}$ é igual a:

Answer 1

Resposta:

a^8 + 1/a^4

$a {}^{4} + \frac{1}{a {}^{4} } = \\ a {}^{4} + \frac{1}{a {}^{4} } \\ \frac{a {}^{4} }{1} \: + \frac{1}{a {}^{4} } \\ \frac{a {}^{4} \times a {}^{4}}{a {}^{4} \times 1 } + \frac{1}{a {}^{4} } \\ a {}^{4} \times a {}^{4} \\ a {}^{4 + 4} \\ a {}^{8} \\ \frac{a {}^{4} \times a {}^{4} }{a {}^{4} \times 1 } + \frac{1}{a {}^{4}} \\ \frac{a {}^{8} }{a {}^{4} \times 1 } + \frac{1}{a {}^{4} } \\ \frac{a {}^{4} \times a {}^{4} }{a {}^{4} \times 1} + \frac{1}{a {}^{4} } \\ \frac{a {}^{8} }{a {}^{4} } + \frac{1}{a {}^{4} } \\ \frac{a {}^{8} + 1 }{a {}^{4} } \\ resposta \\ \frac{a {}^{8} + 1}{a {}^{4} }$