Question

Tìm GTLN của G(x)=3X^2(5-3X^2)

 

Answer 1

\(3x^2\left(5-3x^2\right)\)

\(=15x^2-9x^4\)

\(=-\left(9x^4-2.3.x^2.\frac{5}{2}+\frac{25}{4}-\frac{25}{4}\right)\)

\(=-\left(\left(3x^2-\frac{5}{2}\right)^2-\frac{25}{4}\right)\)

\(=\frac{25}{4}-\left(3x^2-\frac{5}{2}\right)^2\le\frac{5}{2}\)