diketahui [tex]f(x) = a^{2} + a^{-2} [/tex] dan [tex]g(x) = a^{2} - a^{-2} [/tex] Tntukanlah: a. [tex]{f(x)}^{2} - {g(x)^{2} [/tex] b. [tex]g(2x) - f(x) . g

f(x) = a² + a^-2
g(x) = a² - a^-2

a][
f(x)² - g(x)²
= (f(x) + g(x))(f(x) - g(x))
= (a² + a^-2 + a² - a^-2) (a² + a^-2 - a² + a^-2)
= (2 a²) (2 a^-2)
= 4 ✔

b][
g(2x) - f(x) . g(x)
= (2x)² - (2x)^-2 - (a² + a^-2)(a² - a^-2)
= 4x²- 1/(4x²) - (a⁴ - a^-4)
= 1/4 (16x² - x^-2) - a⁴ + a^-4
= 1/4 (16x² - 1/x²) - a⁴ + 1/a⁴ ✔