Question

若实数x,y满足4小于等于x^2+y^2小于等于25

Answer 1

4≤x²+y²≤25.换元,可设x=rcost,y=rsint.(t,r∈R,2≤r≤5.).∴z=x²+y²-xy=r²-(r²/2)sin2t=(r²/2)(2-sin2t).∴zmax=75/2.zmin=2.