Question

Se a^2 + a + 1 = 13 e a^2 - a +1 = 7, então o valor de a^4 + a^2 + 1 é igual a :
(a) 51
(b) 61
(c) 71
(d) 81
(e) 91

Answer 1

$a^2+a+1 =13\\ a^2-a+1 = 7\\ 0a^2-2a+0 = -6\\\\ -2a=-6\\\ a = \frac{6}{2}\\\\ \boxed{a=3}$

$a^4+a^2+1\\\\ 3^4+3^2+1\\\\ 81+9+1\\\\ \boxed{91}$

Alternativa E)

Answer 2

a² + a + 1 = 13 => a² + a = 12
a² - a + 1 = 7 =>    a² - a = 6
                                 2a² = 18 => a² = 9
....................
a⁴ + a² + 1 = a².a² + a² + 1 = 9.9 + 9 + 1 = 81 + 9 + 1 = 91 => LETRA E