①设a＞5,比较√(a-3)-√(a-4)与√(a-4)-√(a-5)的大小②若x＜y＜0,试比较(x^2+y^2)*(x-y)与(x^2-y^2)*(x+y)的大小.
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①设a＞5,比较√(a-3)-√(a-4)与√(a-4)-√(a-5)的大小②若x＜y＜0,试比较(x^+y^)(x-y)与(x^-y^)(x+y)的大小。 解:√(a-3)-√(a-4)=[√(a-3)-√(a-4)][√(a-3)+√(a-4)]/[√(a-3)+√(a-4)]=1/√[(a-3)+√(a-4)]√(a-4)-√(a-5)=[√(a-4)-√(a-5)][√(a-4)+√(a-5)]/[√(a-4)+√(a-5)]=1/[√(a-4)+√(a-5)]1/√[(a-3)+√(a-4)]＞1/[√(a-4)+√(a-5)]∴√(a-3)-√(a-4)＞√(a-4)-√(a-5)解:(x^+y^)(x-y)-(x^-y^)(x+y)=[x^3+xy^-x^y-y^3]-[x^3-xy^+x^y-y^3]=2(xy^-x^y)=2xy(y-x)∵x＜y＜0,∴x＜0,y＜0,(y-x)＞0。即:2xy(y-x)＞0(x^+y^)(x-y)＞(x^-y^)(x+y)。。