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来源：百度知道 编辑：UC知道 时间：2024/05/30 00:43:37
已知3倍根号a+5倍b的绝对值=7（a>0),求s=2倍根号a-3倍b的绝对值的取值范围

谢谢

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

3√a+5|b|=7
|b|=(7-3√a)/5

s=2√2-3|b|=2√2-3(7-3√a)/5
=(10√2-21+9√a)/5
≥(10√2-21)/5