Câu 4:
$A=x^2-6x+11$
$=x^2-6x+9+2$
$=(x-3)^2+2$
$(x-3)^2 \geq 0 ⇔ (x-3)^2+2 \geq 2$
$⇒Min_A=2 ⇔ x-3=0 ⇔ x=3$
$B=2x^2+10x-1$
$B=2\left (x^2+5x-\dfrac{1}{2} \right )$
$B=2\left (x^2+5x+\dfrac{25}{4}-\dfrac{27}{4} \right )$
$B=2\left (x+\dfrac{5}{2} \right )^2-\dfrac{27}{2}$
$2\left (x+\dfrac{5}{2} \right )^2 \geq 0∀x$
$⇒2\left (x+\dfrac{5}{2} \right )^2-\dfrac{27}{2} \geq -\dfrac{27}{2}$
$⇒Min_B=-\dfrac{27}{2} ⇔ x+\dfrac{5}{2}=0 ⇔ x=-\dfrac{5}{2}$
Câu 5 B1:
$-2(3x+2)(3x-2)+5(x+2)^2-(x-1)(2x-1)(2x+1)$
$=-2(9x^2-4)+5(x^2+4x+4)-(x-1)(4x^2-1)$
$=-18x^2+8+5x^2+20x+20-4x^3+x+4x^2-1$
$=-9x^2-4x^3+27+21x$
