Question

已知x>=1,y>=1,且(loga(x))平方+(loga(y))平方=loga(ax平方）+log(ay平方)（a>

Answer 1

(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