已知x+1/x=3,求x的立方+1/x的立方的值,
问题描述：
已知x+1/x=3,求x的立方+1/x的立方的值,
答
∵x+1/x=3
∴x²+1/x²
=(x+1/x)²-2
=3²-2
=9-2
=7
∴x³+1/x³
= (x+1/x)(x²-1+1/x²)
=3*(7-1)
=3*6
=18
答
∵x+1/x=3
∴3³=27=(x+1/x)³=x³+3x²×1/x+3x×1/x²+1/x³=x³+1/x³+3x+3/x=x³+1/x³+3(x+1/x)=x³+1/x³+3×3
∴x³+1/x³=27-9=18
答
解；因为x+1/x=3
所以x²+1/x=(x+1/x)²-2
=3²-2
=9-2
=7
所以x³+1/x³=(x+1/x)(x²-1+1/x²)
=3×(7-1)
=3×6
=18
答
直接x+1/x=3三次方
展开得X^3+(1/X)^3+3(x+1/x)=27
X^3+(1/X)^3=27-9=18
答
x＋1/x＝3
﹙x＋1/x﹚²＝3²
x²＋2＋1/x²＝9
x²＋1/x²＝7
∴x³＋1/x³＝﹙x＋1/x﹚﹙x²－1＋1/x²﹚
＝3×﹙7－1﹚
＝18