x^5+1/x^5怎么化解成（X+1/X）^5-5(x^3+1/x^3)-10(X+1/X)

Question

x^5+1/x^5 怎么化解成（X+1/X）^5-5(x^3+1/x^3) -10(X+1/X)

Answer 1

(a+b)^2=a^2+2ab+b^2(a+b)^3=a^3+3a^2b+3ab^2+b^3(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4(a+b)^5=a^5+5a^4b+10a^3b^2+10a^2b^3+5ab^4+b^5……这是杨辉三角所以(x+1/x)^5=x^5+5x^4(1/x)+10x^3(1/x)^2+10x^2(1/x)^3+5x(1...