(1)f(α)=sinα(6sinα+cosα)+cosα(7sinα-2cosα)
=6(sinα)^2+8sinαcosα-2(cosα)^2
=3(1-cos2α)+4sin2α-(1+cos2α)
=4(sin2α-cos2α)+2
=4(√2)sin(2α-45°)+2,
最大值为4√2+2.
(2)f(A)=4√2sin(2A-45°)+2=6,sin(2A-45°)=1/√2,A为锐角,
∴2A-45°=45°,A=45°.
∴S△ABC=bc/(2√2)=3,bc=6√2,
由余弦定理,a^2=(b+c)^2-2bc(1+cosA)
=(2+3√2)^2-12√2(1+1/√2)
=10,
∴a=√10.