证明不等式:(根号x-根号y)(x-y)≥0(其中x,y皆为正数)
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证明不等式:(根号x-根号y)(x-y)≥0(其中x,y皆为正数)
证明不等式:(根号x-根号y)(x-y)≥0(其中x,y皆为正数)
证明不等式:(根号x-根号y)(x-y)≥0(其中x,y皆为正数)
证明:(√x-√y)(x-y)=(√x-√y)(√x-√y)(√x+√y)=(√x-√y)^2(√x+√y)
因为x,y皆为正数,所以(√x-√y)≥0,(√x+√y)>0
故(√x-√y)^2(√x+√y)≥0
证毕
左边=(根号x-根号y)*[(根号x+根号y)(根号x-根号y)]
=(根号x+根号y)(根号x-根号y)²
显然根号x+根号y>0
根号x-根号y)²≥0
所以(根号x+根号y)(根号x-根号y)²≥0
所以(根号x-根号y)(x-y)≥0
x-y看成(根号x-根号y)(根号x+根号y)原式化为(根号x-根号y)的平方乘以(根号x+根号y)肯定大于等于0