Question

若实数x、y满足2x^2+3y^2=1,s=3x^2-2y^2,则S的取值范围是

Answer 1

根据题意

x^2=(1-3y^2)/2

y^2=(1-2x^2)/3

所以s=3*（1-3y^2)/2-2y^2=3/2-13y^2/2

因为y^2≥0,所以s≤3/2

s=3x^2-2(1-2x^2)/3=13x^2/3-2/3

因为x^2≥0,所以s≥-2/3

所以取值范围为-2/3≤s≤3/2