\(Q=2x^2-6x\)
= [\(\left(\sqrt{2}.x\right)^2-2.\sqrt{2}.x.\dfrac{6}{2\sqrt{2}}+\left(\dfrac{6}{2\sqrt{2}}\right)^2\)] \(-\dfrac{9}{2}\)
\(=\left(\sqrt{2}.x-\dfrac{6}{2\sqrt{2}}\right)^2\) \(-\dfrac{9}{2}\)
Ta có :
\(\left(\sqrt{2}.x-\dfrac{6}{2\sqrt{2}}\right)^2\ge0\)
\(\Rightarrow\left(\sqrt{2}.x-\dfrac{6}{2\sqrt{2}}\right)^2-\dfrac{9}{2}\ge-\dfrac{9}{2}\)
\(\Rightarrow Q\ge-\dfrac{9}{2}\)
\(\Rightarrow Min_Q=-\dfrac{9}{2}\Leftrightarrow\sqrt{2}.x-\dfrac{6}{2\sqrt{2}}=0\)
\(\Rightarrow\sqrt{2}.x-\dfrac{3\sqrt{2}}{2}=0\)
\(\Rightarrow\sqrt{2}.x=\dfrac{3\sqrt{2}}{2}\)
\(\Rightarrow x=\dfrac{3}{2}\)
Q = 2x2 - 6x = 2( x2 - 3x + 9/4) - 9/2 = 2(x - 3/2 )2 -9/2 ≥ - 9/2
Dấu = xảy ra khi ( x- 3/2 )2 = 0 <=> x = 3/2
chúc bn hc tốt 