Jika 2^x-2^(-x)=4, maka 2^2x+2^(-2x)=⋯ dan 2^3x-2^(-3x)=⋯ adalah ?

2^x + 2^-x = 4

Misal 2^x = a dan 2^-x = b
a - b = 4

ab = 2^x . 2^-x = 2^0 = 1

2^2x + 2^-2x = (2^x)^2 + (2^-x)^2
= a^2 + b^2
= (a - b)^2 + 2ab
= 4^2 + 2(1)
= 16 + 2
= 18

2^3x - 2^-3x = (2^x)^3 - (2^-x)^3
= a^3 - b^3
= (a - b)(a^2 + ab + b^2)
= (a - b)(a^2 + b^2 + ab)
= 4(18 + 1)
= 4(19)
= 76