Question

已知实数a,b满足3倍根号a+5倍绝对值b=7，S=2倍根号a-3倍绝对值b，求S的取值范围。

数学题

Answer 1

答案见下图

Answer 2

3√a+5|b|=7
√a=(7-5|b|)/3>=0
7-5|b|>=0
0<=5|b|<=7
0<=|b|<=7/5

S=2√a-3|b|
=2(7-5|b|)/3-3|b|
=(14-19|b|)/3

0<=|b|<=7/5
-7/5<=-|b|<=0
-133/5<=-19|b|<=0
14-133/5<=14-19|b|<=14+0
-63/5<=14-19|b|<=14
-21/5<=(14-19|b|)/3<=14/3

所以-21/5<=S<=14/3

Answer 3

3sqrt(a)+5|b|=7
S=2sqrt(a)-3|b|
不妨令sqrt(a)=c,|b|=d,c,d>=0
3c+5d=7,d<=7/5
S=2c-3d=14/3-19d/3
S取值范围为(-21/5,14/3)这个好一些