已知x^2+x^-2=4,求x^6+x^-6

(x^2+x^-2)^3=4^3
x^6+x^-6+x^2+x^-2=64
x^6+x^-6=64-4
x^6+x^-6=60

(x^2+x^-2)^3=4^3
x^6+3x^4x^(-2)+3x^(-4)x^2+x^-6=64
x^6+3x^2+3x^-2+x^-6=64
x^6+x^-6+12=64
x^6+x^-6=52

主要用到(a+b)^3=a^3+3a^2b+3ab^2+b^3这公式,自己再推下

(a+b)^3 = a^3 +3(a^2)b +3a(b^2) +b^3(和的立方公式)