已知x>y>0,log3(x-y/2)^2=log3(xy),则log3(根号x/y-根号2)多少
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已知x>y>0,log3(x-y/2)^2=log3(xy),则log3(根号x/y-根号2)多少已知x>y>0,log3(x-y/2)^2=log3(xy),则log3(根号x/y-根号2)多少已知
已知x>y>0,log3(x-y/2)^2=log3(xy),则log3(根号x/y-根号2)多少
已知x>y>0,log3(x-y/2)^2=log3(xy),则log3(根号x/y-根号2)多少
已知x>y>0,log3(x-y/2)^2=log3(xy),则log3(根号x/y-根号2)多少
答:
因为:x>y>0
因为:log3 (x-y/2)^2 =log3(xy)
所以:(x-y/2)^2=xy>0
所以:x^2-xy+(y^2)/4=xy
所以:x^2-2xy+(y^2) /4=0
所以:(x-y)^2=(3/4)y^2
解得:x-y=(√3/2)y(负值不符合舍弃)
所以:x/y=(2+√3) /2
所以:
log3 [ √(x/y)-√2 ]
=log3 [ (2+√3)/2 -√2]
=log3 [ (2+√3-2√2) /2 ]
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