Question

Se 2 (elevado) x + 2 (elevado)x negativo= a, então qual o valor de 4(elevado)x + 4 (elevado) x negativo?

Answer 1

$2^{x} + 2^{-x} = a$
$(2^{x} + 2^{-x})^{2} = a^{2}$
$(2^{x})^{2} + 2*2^{x}*2^{-x} + (2^{-x})^{2} = a^{2}$
$(2^{2})^{x} + 2^{1+x-x} + (2^2)^{-x} = a^{2}$
$(2^{2})^{x} + 2^{1} + (2^2)^{-x} = a^{2}$
$(2^{2})^{x} + (2^2)^{-x} = a^{2} - 2$

$4^{x} + 4^{-x}$
$(2^{2})^{x} + (2^{2})^{-x}$

Como $(2^{2})^{x} + (2^2)^{-x} = a^{2} - 2$:

$4^{x} + 4^{-x} =(2^{2})^{x} + (2^{2})^{-x} =a^{2} - 2$
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Resposta:
$4^{x} + 4^{-x}=a^{2} - 2$