a) \(A=x^2-4x-2=\left(x^2-4x+4\right)-6=\left(x-2\right)^2-6\ge-6\left(\forall x\right)\)
Dấu "=" xảy ra khi: \(\left(x-2\right)^2=0\Rightarrow x=2\)
Vậy Min(A) = -6 khi x = 2
b) \(B=\left(x-1\right)\left(2x+3\right)-12\)
\(B=2x^2+x-3-12\)
\(B=2\left(x^2+\frac{x}{2}+\frac{1}{16}\right)-\frac{121}{8}\)
\(B=2\left(x+\frac{1}{4}\right)^2-\frac{121}{8}\ge-\frac{121}{8}\left(\forall x\right)\)
Dấu "=" xảy ra khi: \(2\left(x+\frac{1}{4}\right)^2=0\Rightarrow x=-\frac{1}{4}\)
Vậy \(Min_B=-\frac{121}{8}\Leftrightarrow x=-\frac{1}{4}\)
A = x2 - 4x - 2
= ( x2 - 4x + 4 ) - 6
= ( x - 2 )2 - 6 ≥ -6 ∀ x
Đẳng thức xảy ra <=> x - 2 = 0 => x = 2
=> MinA = -6 <=> x = 2
B = ( x - 1 )( 2x + 3 ) - 12
= 2x2 + x - 3 - 12
= 2x2 + x - 15
= 2( x2 + 1/2x + 1/16 ) - 121/8
= 2( x + 1/4 )2 - 121/8 ≥ -121/8 ∀ x
Đẳng thức xảy ra <=> x + 1/4 = 0 => x = -1/4
=> MinB = -121/8 <=> x = -1/4
Ta có : \(A=x^2-4x-2\)
\(=\left[x^2-2\cdot x\cdot2+2^2\right]-6\)
\(=\left(x-2\right)^2-6\)
Vì \(\left(x-2\right)^2\ge0\forall x\)
=> \(\left(x-2\right)^2-6\ge-6\forall x\)
Dấu " = " xảy ra khi và chỉ khi (x - 2)2 = 0 => x = 2
Vậy \(A_{min}=-6\)khi x = 2
\(B=\left(x-1\right)\left(2x+3\right)-12\)
\(B=x\left(2x+3\right)-1\left(2x+3\right)-12\)
\(B=2x^2+3x-2x-3-12\)
\(B=2x^2+x-15\)
\(B=2\left(x^2+\frac{1}{2}x-\frac{15}{2}\right)\)
\(B=2\left[x^2+2\cdot x\cdot\frac{1}{4}+\left(\frac{1}{4}\right)^2\right]-\frac{121}{8}\)
\(B=2\left(x+\frac{1}{4}\right)^2-\frac{121}{8}\)
Vì \(\left(x+\frac{1}{4}\right)^2\ge0\forall x\)
=> \(2\left(x+\frac{1}{4}\right)^2-\frac{121}{8}\ge-\frac{121}{8}\forall x\)
Dấu " = " xảy ra khi và chỉ khi (x + 1/4)2 = 0 => x = -1/4
Vậy \(B_{min}=-\frac{121}{8}\)khi x = -1/4
Ta có A = x2 - 4x - 2 = (x2 - 4x + 4) - 6 = (x - 2)2 - 6 \(\ge\)-6
Dấu "=" xảy ra <=> x - 2 = 0
=> x = 2
Vậy Min A = -6 <=> x = 2
Ta có B = (x - 1)(2x + 3) - 12
= 2x2 + x - 15
= \(2\left(x^2+\frac{1}{2}x-\frac{15}{2}\right)=2\left(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{121}{16}\right)=2\left(x+\frac{1}{4}\right)^2-\frac{121}{8}\ge-\frac{121}{8}\)
Dấu "=" xảy ra <=> x + 1/4 = 0
=> x = -1/4
Vậy Min B = -121/8 <=> x = -1/4