Question

Nao consigo responder essa questao: seja 3^x+3^-x=15,entao 9^x+9^-x será

Answer 1

eleva os dois lados ao quadrado
lembrando que: (a+b)² = a²+2.a.b + b²

$3^x + 3^{-x} = 15\\\\ (3^{x}+3^{-x})^2 = 15^2\\\\ (3^x)^2+2*3^x*3^{-x} + (3^{-x})^2 = 15^2\\\\9^x +2*3^{x-x} + 9^{-x} =225\\\\9^x+2*3^0 + 9^{-x}=225\\\\9^x+2*1+9^{-x}=225\\\\9^x+2+9^{-x}=225\\\\9^x +9^{-x} = 225-2\\\\9^x+9^{-x}=223$