已知向量→m=（COS平方X,根号3）,→n=(2,sin2X),函数f(x)=→m乘→n. （1）求F(x)的单调递增

f(x)=2(cosx)^2+ √3sin2x
=cos2x+√3sin2x+1
=2(sinπ/6cos2x+cosπ/6sin2x)+1
=2sin(2x+π/6）+1,
2kπ-π/2≤2x+π/6≤2kπ+π/2,单调递增区间,
2kπ-2π/3≤2x≤2kπ+π/3,k∈Z,
kπ-π/3≤x≤kπ+π/6,k∈Z,
x∈[kπ-π/3,kπ+π/6],单调递增.
2、f(C)=2sin(2C+π/6）+1=3,
sin(2C+π/6)=1,
2C+π/6=π/2,
C=π/6,
S△ABC=(absinC)/2=ab/4=√3/2,
ab=2√3,(1)
根据余弦定理,
c^2=a^2+b^2-2abcosC,
a^2+b^2- √3ab=1,(2)
(1)代入（2）,
a^2+b^2=7,(3)
(3)+(1)*2,
(a+b)^2=(2+√3）^2,
a+b=2+ √3,
∴ a=2,b=√3.