Докажите неравенство: 6y-9y^2-4<0.

Ответ:

\[6y - 9y^{2} - 4 < 0\]

\[- \left( 9y^{2} - 6y + 4 \right) < 0\]

\[- \left( 9y^{2} - 6y + 1 + 3 \right) < 0\]

\[- \left( (3y - 1)^{2} + 3 \right) < 0\]

\[(3y - 1)^{2} \geq 0;\ \ 3 > 0;\ \ \]

\[\left( - (3y - 1)^{2} + 3 \right) < 0 \Longrightarrow верно.\]