Question

докажите неравенства 10x^2-6xy+y^2-4x^2+6>0

Answer 1

10x^2-4x^2-6xy+6+y^2>0
6x^2-6xy+6+y2>0
6x^2+6-6xy+y^2>0
6(x^2-1)-6y(x-y)>0
(6-6y)(x^2-1)(x-y)>0
6(x-1)(x+1)>0 |/6
(x-1)>0       x+1>0
x>1             x>-1
            ///////////////////////////
------(-1)--------(1)---------->
(-1;1) и (1;+ бесконечности)