复合二次根式的化简``______________ `√2+ ----------- ````√2+ ------- ````````√2+……("``"无义,只是为了占格)可用配方法
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复合二次根式的化简``______________ `√2+ ----------- ````√2+ ------- ````````√2+……("``"无义,只是为了占格)可用配方法
复合二次根式的化简
``______________
`√2+ -----------
````√2+ -------
````````√2+……
("``"无义,只是为了占格)
可用配方法
复合二次根式的化简``______________ `√2+ ----------- ````√2+ ------- ````````√2+……("``"无义,只是为了占格)可用配方法
设原式=x
则x^2=2+x
即有x^2-x-2=0,(x+1)(x-2)=0
由于x>0,所以x=2
即``______________
`√2+ -----------
````√2+ -------
````````√2+……
=2
o
令原式=x
则1/(x+根号2)=x (根据根号是无限层的特点)
所以解得x=-1/2*2^(1/2)-1/2*6^(1/2)或-1/2*2^(1/2)+1/2*6^(1/2)
但显然原式>0
所以x=-1/2*2^(1/2)+1/2*6^(1/2)
设原式=a,则a^2=2+a,解方程得a=2,a=-1(小于0,舍)
所以原式=2