已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和...已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和最小值

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已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和...已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和最小值

已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和...已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和最小值
已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和...
已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和最小值

已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和...已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方)+log(ay平方)(a>1)求loga(xy)的最大值和最小值
(loga(x))^2 + (loga(y))^2 = loga(ax^2) + loga(ay^2) = loga(a) + 2loga(x) + loga(a) + 2loga(y) = 2+2loga(y)
[loga(x)]^2 + [loga(y)-1]^2 = 1
loga(xy) = loga(x) + loga(y)
最大值=1+√2
最小值=1-√2

(logax)²+(logay)²=loga(ax²)+loga(ay²)=2logax+1+2logay+1
所以(logax-1)²+(logay-1)²=4
则logax=1+2cosb,logay=1+2sinb
loga(xy)=2+2cosb+2sinb=2+2√2*sin(b+π/4)
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