\(A=-4t^2+3t-3\)
\(=-\left(4t^2-3t+3\right)\)
\(=-\left\{\left[\left(2t\right)^2-2.2t.\frac{3}{4}+\left(\frac{3}{4}\right)^2\right]-\left(\frac{3}{4}\right)^2+3\right\}\)
\(=-\left[\left(2t-\frac{3}{4}\right)^2-\frac{9}{16}+\frac{48}{16}\right]\)
\(=-\left(2t-\frac{3}{4}\right)^2-\frac{39}{16}\)
\(Có:\left(2t-\frac{3}{4}\right)^2\ge0\) \(\text{với mọi x}\)
\(\Rightarrow-\left(2t-\frac{3}{4}\right)^2\le0\text{ với mọi x}\)
\(\Rightarrow-\left(2t-\frac{3}{4}\right)^2-\frac{39}{16}\le0-\frac{39}{16}=-\frac{39}{16}\text{ với mọi x}\)
\(\text{=> GTLN của biểu thức A là }-\frac{39}{16}\)
khi \(2t-\frac{3}{4}=0\) hay \(t=\frac{3}{8}\)
\(B=4k^2+3k-3\)
\(=\left[\left(2k\right)^2+2.2k.\frac{3}{4}+\left(\frac{3}{4}\right)^2\right]-\left(\frac{3}{4}\right)^2-3\)
\(=\left(2k+\frac{3}{4}\right)^2-\frac{9}{16}-\frac{48}{16}\)
\(=\left(2k+\frac{3}{4}\right)^2-\frac{57}{16}\)
\(Có:\left(2k+\frac{3}{4}\right)^2\ge0\) \(\text{với mọi x}\)
\(\Rightarrow\left(2k+\frac{3}{4}\right)^2-\frac{57}{16}\ge0-\frac{57}{16}=-\frac{57}{16}\text{với mọi x}\)
\(\Rightarrow\text{GTNN của biểu thức B là }-\frac{57}{16}\)
khi \(2k+\frac{3}{4}=0\) hay \(k=\frac{3}{8}\)
\(A=-4t^2+3t-3\)
\(=-\left(4t^2-3t+3\right)\)
\(=-\left\{\left[\left(2t\right)^2-2.2t.\frac{3}{2}+\left(\frac{3}{2}\right)^2\right]-\left(\frac{3}{2}\right)^2+3\right\}\)
\(=-\left[\left(2t-\frac{3}{2}\right)^2-\frac{9}{4}+\frac{12}{4}\right]\)
\(=-\left(2t-\frac{3}{2}\right)^2-\frac{3}{4}\)
\(Có:\left(2t-\frac{3}{2}\right)^2\ge0\) \(\text{với mọi x}\)
\(\Rightarrow-\left(2t-\frac{3}{2}\right)^2\le0\text{ với mọi x}\)
\(\Rightarrow-\left(2t-\frac{3}{2}\right)^2-\frac{3}{4}\le0-\frac{3}{4}=-\frac{3}{4}\text{ với mọi x}\)
\(\Rightarrow\text{GTLN của biểu thức A là}-\frac{3}{4}\)
khi \(2t-\frac{3}{2}=0\) hay \(t=\frac{3}{4}\)