已知x+1/x=3.求下列各式的值,(1)x²+1/x²,(2)x³+1/x³,(3)x²/x的四次方+x²+1
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/24 23:28:37
![已知x+1/x=3.求下列各式的值,(1)x²+1/x²,(2)x³+1/x³,(3)x²/x的四次方+x²+1](/uploads/image/z/5233674-66-4.jpg?t=%E5%B7%B2%E7%9F%A5x%2B1%2Fx%3D3.%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%2C%EF%BC%881%EF%BC%89x%26sup2%3B%2B1%2Fx%26sup2%3B%2C%EF%BC%882%EF%BC%89x%26sup3%3B%2B1%2Fx%26sup3%3B%2C%EF%BC%883%EF%BC%89x%26sup2%3B%2Fx%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2Bx%26sup2%3B%2B1)
已知x+1/x=3.求下列各式的值,(1)x²+1/x²,(2)x³+1/x³,(3)x²/x的四次方+x²+1
已知x+1/x=3.求下列各式的值,
(1)x²+1/x²,(2)x³+1/x³,(3)x²/x的四次方+x²+1
已知x+1/x=3.求下列各式的值,(1)x²+1/x²,(2)x³+1/x³,(3)x²/x的四次方+x²+1
(1)x²+1/x²=x²+2+1/x²-2=(x+1/x)²-2=3²-2=7,
(2)x³+1/x³=(x+1/x)(x²-1+1/x²)=3×(7-1)=18,
(3)x²/x的四次方+x²+1=1/(x²+1+1/x²)=1/(7+1)=1/8
x²+1/x²=(x+1/x)^2-2=7
x³+1/x³=(x+1/x)(x^2-2+1/x^2)=15
x²/x的四次方+x²+1=1/(x^2+1+1/x^2)=1/8