Question

(x+1/x)的立方等于多少？

Answer 1

可以利用和的立方公式展开(a+b)³=a³+3a²b+3ab²+b³
由和的立方公式可得(x+1/x)³=x³+3x²*1/x+3x*(1/x)²+(1/x)³
=x³+3x+3/x+1/x³

Answer 2

∵ (a+b)³ =(a+b)(a+b)²
=(a+b)(a²+2ab+b²)
=a³+2a²b+ab²+a²b+2ab²+b³
=a³+3a²b+3ab²+b³
∴ （x+1/x）³
=x³+3x+3/x+1/x³

Answer 3

( x＋1/x)³=( x²/ x+1/x)³
=[( x²+1)/x]³
=( x²+1)³/x³
=( x²+1)²( x²+1)/ x³
=(x^4+2x²+1)( x²+1)/ x³
= (x^8+ x^4+2x^4+2x²+ x²+1)/ x³