二次根式的化简求值(最新整理)

1、二次根式的化简求值【知识梳理】二次根式化简求值就是运用整体代入、分解变形、构造关系式或图形等重要的技巧与方法，解题的关键是，有时需把已知条件化简，或把已知条件变形；有时需把待求式化简或变形；有时需把已知条件和待求式同时变形。5 +55 -5【例题精讲】【例 1】设 x =， y =，求 x6 + y 6 的值。【巩固】1、设 x =2 - 1，y =2 + 1，求 x 2 - xy + y 2 的值。2 + 12 - 112 -31112、已知 x =2 +，y =3，求(x + 1)2 + (y + 1)2 的值。3xx 2 + 3x + 1【拓展】已知 x = 2 -，求 x4 - 5x3

2、 + 6x2 - 5x 的值。xx【例 2】已知+ 1 = 2 ， 那么-xx 2 + 9x + 1的值等于。【巩固】xa1、若= 1 -a4x + x 2，则的值为（）a. a - 1ab. 1 - a ac. a + 1ad. 不能确定xx52、已知+ 1 =，求- 的值。xx 2 + x + 1xx 2 - x + 1【例 3】已知 a、b 是实数，且(1 + a 2 + a)(1 + b 2 + b)= 1 ，问 a、b 之间有怎样的关系？请推导。【巩固】已知(x +x 2 + 2008 )(y +y 2 + 2008 )= 2008 ，求x 2 - 3xy - 4 y 2 - 6x

3、- 6 y + 58 的值。a 2 + 4b 2 + 1【例 4】已知 a、b 均为正数，且 a + b = 2 ，求u =+的最小值x 2 + 4(12 - x)2 + 9【巩固】求代数式+的最小值。“”“”at the end, xiao bian gives you a passage. minand once said, people who learn to learn are very happy people. in every wonderful life, learning is an eternal theme. as a professional clerical and

4、 teaching position, i understand the importance of continuous learning, life is diligent, nothing can be gained, only continuous learning can achieve better self. only by constantly learning and mastering the latest relevant knowledge, can employees from all walks of life keep up with the pace of enterprise development and innovate to meet the needs of the market. this document is also edited by my studio professionals, there may be e