Toán 9 Tìm gtln, gtnn

Max sử dụng Buchiacopxki
[tex]2\sqrt{x}+\dfrac{3}{2}\sqrt{1-x} \leq \sqrt{\left(4+\dfrac{9}{4}\right)(x+1-x)}[/tex]
Min: ĐKXĐ [tex]0 \leq x \leq 1[/tex]
[tex]a=\sqrt{4x}+\sqrt{\dfrac{9}{4}-\dfrac{9x}{4}}+\dfrac{7}{2} \geq \sqrt{4x+\dfrac{9}{4}-\dfrac{9x}{4}}+\dfrac{7}{2}[/tex]
[tex]a\geq \sqrt{\dfrac{9}{4}+\dfrac{7x}{4}}+\dfrac{7}{2} \geq \sqrt{\dfrac{9}{4}}+\dfrac{7}{2}=5[/tex]
Dấu "=" xảy ra khi [tex]x=0[/tex]