观察下列各式:a+b=1,a^2+b^2=3,a^3+b^3=4,a^4+b^4=7,a^5+b^5=11...则a^10+b^10=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/26 19:50:16
观察下列各式:a+b=1,a^2+b^2=3,a^3+b^3=4,a^4+b^4=7,a^5+b^5=11...则a^10+b^10=?
x){Ovt?tB=JN5I3N35,c[ 25L,S[CC==3 6IE1XΆnf=ݹٴA5eCs km$$YgÓKⶆƶFIimF5'74B6i|@FI Cm @

观察下列各式:a+b=1,a^2+b^2=3,a^3+b^3=4,a^4+b^4=7,a^5+b^5=11...则a^10+b^10=?
观察下列各式:a+b=1,a^2+b^2=3,a^3+b^3=4,a^4+b^4=7,a^5+b^5=11...则a^10+b^10=?

观察下列各式:a+b=1,a^2+b^2=3,a^3+b^3=4,a^4+b^4=7,a^5+b^5=11...则a^10+b^10=?
a+b=1
平方
a²+2ab+b²=1
所以2ab=1-3=-2
ab=-1
a^5+b^5=11
平方
a^10+2a^5b^5+b^10=121
所以原式=121-2(ab)^5=123