思路三角换元.
因x²+y²=1,故可设x=cost,y=sint,(t∈R),
3x-4y=3cost-4sint
=5cos(t+ψ) (sinψ=4/5,cosψ=3/5).
-1≤cos(t+ψ)≤1,
===>-5≤5cos(t+ψ)≤5.
===>(3x-4y)max=5