\(E=2x^2+4x+13\)
\(=2\left(x^2+2x+\dfrac{13}{2}\right)\)
\(=2\left(x^2+2x+1+\dfrac{11}{2}\right)\)
\(=2\left(x+1\right)^2+11>=11>0\forall x\)
\(F=2x^2-3x+6\)
\(=2\left(x^2-\dfrac{3}{2}x+3\right)\)
\(=2\left(x^2-2\cdot x\cdot\dfrac{3}{4}+\dfrac{9}{16}+\dfrac{39}{16}\right)\)
\(=2\left(x-\dfrac{3}{4}\right)^2+\dfrac{39}{8}>=\dfrac{39}{8}>0\forall x\)
E=2x2+4x+13
E=2(x2+2x+1)+11
E=2(x+1)2+11
2(x+1)2≥0,∀x
⇒2(x+1)2+11 lớn hơn 0 ∀x
⇒E luôn nhân giá trị dương
F=2x2-3x+6
2F=4x2-6x+12
2F=(4x2-6x+\(\dfrac{9}{4}\))+\(\dfrac{15}{4}\)
2F=(2x+\(\dfrac{3}{2}\))2+\(\dfrac{15}{4}\)
F=\(\dfrac{\left(2x+\dfrac{3}{2}\right)^2}{2}\)+\(\dfrac{15}{8}\)
\(\dfrac{\left(2x+\dfrac{3}{2}\right)^2}{2}\)≥0,∀x
⇒\(\dfrac{\left(2x+\dfrac{3}{2}\right)^2}{2}\)+\(\dfrac{15}{8}\) lớn hơn 0 ∀x
⇒F luôn nhận giá trị dương
