Question

已知正数x,y满足|lgx/y|≤1且|lg(x^2y)|≤1,求xy的取值范围

Answer 1

|lgx/y|≤1 =>1/10≤x/y≤10 1)

|lg(x^2y)|≤1 =>1/10≤x^2y≤10 2)

1)÷2）,得

1/100≤xy^2≤100 3)

2)*3),得 1/1000≤(xy)^3≤1000

所以 1/10≤xy≤10