Question

已知-1＜a+b＜3且2＜a-b＜4,求2a+3b的取值范围.

Answer 1

-＜2a+3b＜

解析:

设2a+3b=m(a+b)+n(a-b),

∴,                                                         4分

∴m=,n=-.                                                        6分

∴2a+3b=(a+b)-(a-b).                                             7分

∵-1＜a+b＜3,2＜a-b＜4,

∴-＜(a+b)＜,-2＜-(a-b)＜-1,                               10分

∴-＜(a+b)- (a-b)＜,                                       12分

即-＜2a+3b＜.                                                   14分