Question

已知2lgx-y/2=lgx+lgy,求log（3-2 ）x/y的值

Answer 1

2lg(x-y)/2=lgx+lgy

(x+y)^2/4=x*y 两者都除以y^2

得 (x/y)^2-6*x/y+1=0

x/y=3+2√2或x/y=3-2√2

当x/y=3+2√2时,log以(3-2√2)为底,x/y的值=log(3-2√2)[3+2√2]

当x/y=3-2√2时,log以(3-2√2)为底,x/y的值=1