已知X+1/X=3 1X^+1/X^=?X的3次方+1/(X的3次方)=?X的4次方+1/(X的4次方) X的5次方+1/(X的5次方)快好的还有赏

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/16 00:04:31

已知X+1/X=3 1X^+1/X^=?X的3次方+1/(X的3次方)=?X的4次方+1/(X的4次方) X的5次方+1/(X的5次方)快好的还有赏
已知X+1/X=3 1X^+1/X^=?X的3次方+1/(X的3次方)=?X的4次方+1/(X的4次方) X的5次方+1/(X的5次方)
快好的还有赏

已知X+1/X=3 1X^+1/X^=?X的3次方+1/(X的3次方)=?X的4次方+1/(X的4次方) X的5次方+1/(X的5次方)快好的还有赏
x+1/x=3
x²+1/x²=(x+1/x)²-2=7
x³+1/x³=(x+1/x)(x²-1+1/x²)=18
x^4+1/x^4=(x²+1/x²)²-2=47
x^5+1/x^5=(x+1/x)(x^4-x²+1-1/x²+1/x^4)=120

X^+1/X^=7,X的3次方+1/(X的3次方)=18, X的4次方+1/(X的4次方)=47, X的5次方+1/(X的5次方)=123,

3x^2+9x+3=0
x=(-3+-√5)/2
x^3+1/x^3=(x^9+1)/x^3=8[(-3+-√5)^9/2^9+1]/(-3+-√5)^3
x^4+1/x^4=(x^16+1)/x^4=16[(-3+-√5)^16/2^16+1]/(-3+-√5)^4
x^5+1/x^5=(x^25+1)/x^5=32[(-3+-√5)^25/2^25+1]/(-3+-√5)^5