若a,b满足3a^2+5|b|=7,s=2a^2-3|b|,则s的取值范围是______.

题目

若a,b满足3a^2+5|b|=7,s=2a^2-3|b|,则s的取值范围是______.

答案

3a^2+5|b|=7
a^2=(7-5|b|)/3≥0,
0≤3|b|≤21/5
|b|=(7-3a^2)/5≥0,
0≤2a^2≤14/3
s=2a^2-3|b|,
Smax=14/3-0,Smin=0-21/5
-21/5≤S≤14/3,