作业帮二次根式化简和求值一题化简再求值：[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)其中x是满足方程x-4√x +1=0的值要有过程（有个思路也行）!请重点解释：“x-4√x +1=0”如何去用！
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 17:49:04
![二次根式化简和求值一题化简再求值：[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)其中x是满足方程x-4√x +1=0的值要有过程（有个思路也行）!请重点解释：“x-4√x +1=0”如何去用！](/uploads/image/z/5157996-60-6.jpg?t=%E4%BA%8C%E6%AC%A1%E6%A0%B9%E5%BC%8F%E5%8C%96%E7%AE%80%E5%92%8C%E6%B1%82%E5%80%BC%E4%B8%80%E9%A2%98%E5%8C%96%E7%AE%80%E5%86%8D%E6%B1%82%E5%80%BC%EF%BC%9A%5B%28x%5E2-5%29%2F%28x-1%29%2B1%5D%2A%5B%28x%5E3-1%29%2Fx%5E2-2x%5D%2F%28x%2B3%29%E5%85%B6%E4%B8%ADx%E6%98%AF%E6%BB%A1%E8%B6%B3%E6%96%B9%E7%A8%8Bx-4%E2%88%9Ax+%2B1%3D0%E7%9A%84%E5%80%BC%E8%A6%81%E6%9C%89%E8%BF%87%E7%A8%8B%EF%BC%88%E6%9C%89%E4%B8%AA%E6%80%9D%E8%B7%AF%E4%B9%9F%E8%A1%8C%EF%BC%89%21%E8%AF%B7%E9%87%8D%E7%82%B9%E8%A7%A3%E9%87%8A%EF%BC%9A%E2%80%9Cx-4%E2%88%9Ax+%2B1%3D0%E2%80%9D%E5%A6%82%E4%BD%95%E5%8E%BB%E7%94%A8%EF%BC%81)
二次根式化简和求值一题化简再求值：[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)其中x是满足方程x-4√x +1=0的值要有过程（有个思路也行）!请重点解释：“x-4√x +1=0”如何去用！
二次根式化简和求值一题
化简再求值：
[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)
其中x是满足方程x-4√x +1=0的值
要有过程（有个思路也行）!
请重点解释：“x-4√x +1=0”如何去用！
二次根式化简和求值一题化简再求值：[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)其中x是满足方程x-4√x +1=0的值要有过程（有个思路也行）!请重点解释：“x-4√x +1=0”如何去用！
x-4√x +1=0
x-4√x +4-3=0
(√x-2)^2=3
√x=2+√3或√x=2-√3
x=7+4√3或x=7-4√3
[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)
=（x^2+x-6)/(x-1)*[(x-1)(x^2+x+1)/x(x-2)]/(x+3)
=[(x-2)(x+3)(x-1)(x^2+x+1)]/[x(x-1)(x-2)(x+3)]
=(x^2+x+1)/x
=x+1+1/x
当x=7+4√3时,
原式=7+4√3+1+7-4√3
=15
当x=7-4√3+1+7+4√3
=15
[(x^2-5)/(x-1)+1]*[(x^3-1)/x^2-2x]/(x+3)
=（x^2+x-6)/(x-1)*[(x-1)(x^2+x+1)/x(x-2)]/(x+3)
=[(x-2)(x+3)(x-1)(x^2+x+1)]/[x(x-1)(x-2)(x+3)]
=(x^2+x+1)/x
=x+1+1/x
当x=7+4√3时，
原式=7+4√3+1+7-4√3
=15
当x=7-4√3+1+7+4√3
=15
OK
x-4√x +1=0
x-4√x +4-3=0
(√x-2)^2=3
√x=2+√3或√x=2-√3
x=7+4√3或x=7-4√3
当x=7+4√3时，
原式=7+4√3+1+7-4√3
=15
当x=7-4√3+1+7+4√3
=15