Question

(mx+nx)^2<=(m^2+n^2)(x^2+y^2), inegalitate, m,n,x,y apartin lui R

Answer 1

[tex](mx+ny)^2\leq(m^2+n^2)(x^2+y^2)\\ m^2x^2+n^2y^2+2mnxy \leq m^2x^2+m^2y^2+n^2x^2+n^2y^2\\ 2mnxy\leq m^2y^2+n^2x^2\\ m^2y^2+n^2x^2-2mnxy\leq 0\\ (my-nx)^2\leq 0[/tex]