已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1
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![已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1](/uploads/image/z/6934504-40-4.jpg?t=%E5%B7%B2%E7%9F%A5y%26%23178%3B-3y%2B1%3D0%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%88%86%E5%BC%8F%E7%9A%84%E5%80%BC+y%26%23178%3B%2B%EF%BC%881%2Fy%26%23178%3B%EF%BC%89+y%26%23178%3B%2Fy%E7%9A%844%E6%AC%A1%E6%96%B9%2By%26%23178%3B%2B1%E5%B7%B2%E7%9F%A5y%26%23178%3B-3y%2B1%3D0%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%88%86%E5%BC%8F%E7%9A%84%E5%80%BC+y%26%23178%3B%2B%EF%BC%881%2Fy%26%23178%3B%EF%BC%89+y%26%23178%3B%2Fy%E7%9A%844%E6%AC%A1%E6%96%B9%2By%26%23178%3B%2B1)
已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1
已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1
已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1
已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1已知y²-3y+1=0,求下列分式的值 y²+(1/y²) y²/y的4次方+y²+1
解
y²-3y+1=0
两边除以y得:
y-3+1/y=0
即y+1/y=3
两边平方得:
(y+1/y)²=9
y²+2+1/y²=9
∴y²+1/y²=7
y²/(y^4+y²+1]
=1/(y²+1+1/y²)
=1/(7+1)
=1/8