Question Number 63539 by REHEMAABDDUL last updated on 05/Jul/19
$$\mathrm{The}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}\:\mathrm{is}\:\_\_\_. \\ $$
Commented by Prithwish sen last updated on 05/Jul/19
$$=\:\mathrm{2}\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} +\frac{\mathrm{7}}{\mathrm{8}} \\ $$$$\because\:\mathrm{2}\left(\mathrm{x}−\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$$\therefore\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value}\:=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$
Commented by meme last updated on 05/Jul/19
$${a}=\mathrm{2}>\mathrm{0} \\ $$$${the}\:{minimum}\:{is}\:{x}=\frac{\mathrm{3}}{\mathrm{4}} \\ $$
Answered by Rio Michael last updated on 05/Jul/19
$$\:{min}\:{value}\:=\:\frac{\mathrm{4}{ac}−{b}^{\mathrm{2}} }{\mathrm{4}{a}} \\ $$$$\:\:{min}\:{val}=\:\frac{\mathrm{4}\left(\mathrm{2}\right)\left(\mathrm{2}\right)−\left(−\mathrm{3}\right)^{\mathrm{2}} }{\mathrm{4}\left(\mathrm{2}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$