Question

2a+5=(a-3)A+(a-2)B，求2A+B的值

Answer 1

2a+5
=Aa-3A+Ba-2B
=(A+B)a+(-3A-2B)
所以A+B=2
-3A-2B=5
B=11
A=-9
2A+B=-7

Answer 2

过（0，1）
1=a+b

0<=x<=π/4
π/4<=x+π/4<=π/2
所以√2/2<=sin(x+π/4)<=1
若b>0
则最大=a+√2b=2√2-1
a+b=1
则a=-1,b=2

若b<0
则最大=a+b=2√2-1
和a+b=1矛盾

所以f(x)=-1+2√2sin(x+π/4)