Question

已知x^2+y^2 =a^2 (a>0) 求|xy|的最大值

Answer 1

令：x=asinb,y=acosb
|xy|=|a^2sinbcosb|=|a^2*(sin2b)/2|
所以最大值：a^2/2

Answer 2

a^2=x^2+y^2 =|x|^2+|y|^2 >=2|x||y|=2|xy|
|xy|<=a^2/2 (在|x|=|y|=a/根号2处取等号)
|xy|的最大值=a^2/2