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\(S=\dfrac{3x^2+8x+6}{x^2+2x+1}=\dfrac{-2\left(x^2+2x+1\right)+x^2+4x+4}{x^2+2x+1}=-2+\left(\dfrac{x+2}{x+1}\right)^2\ge-2\)
\(S_{min}=-2\) khi \(x=-2\)
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7x( 2 - 3x ) + x2( 2x + 1 ) - 2x2( x - 2 ) + 2x( 8x - 7 )
= 14x - 21x2 + 2x3 + x2 - 2x3 + 4x2 + 16x2 - 14x
= ( 2x3 - 2x3 ) + ( -21x2 + x2 + 4x2 + 16x2 ) + ( 14x - 14x )
= 0
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a) \(A= 2x^2- 3x +1\)
\(=2\left(x^2-\dfrac{3}{2}x+\dfrac{1}{2}\right)\)
\(=2\left(x^2-2\cdot x\cdot\dfrac{3}{4}+\dfrac{9}{16}-\dfrac{1}{16}\right)\)
\(=2\left(x-\dfrac{3}{4}\right)^2-\dfrac{1}{8}\ge-\dfrac{1}{8}\)
Vậy Amin = \(-\dfrac{1}{8}\) khi \(x=\dfrac{3}{4}\)
b) \(B= 4x^2 +7x + 13\)
\(=\left(2x\right)^2+2\cdot2x\cdot\dfrac{7}{4}+\dfrac{49}{16}+\dfrac{159}{16}\)
\(=\left(2x+\dfrac{7}{4}\right)^2+\dfrac{159}{16}\ge\dfrac{159}{16}\)
Vậy Bmin = \(\dfrac{159}{16}\) khi \(x=-\dfrac{7}{8}\)
c) \(C= 5-8x+x^2\)
\(=x^2-2\cdot x\cdot4+16+9\)
\(=\left(x-4\right)^2+9\ge9\)
Vậy Cmin = 9 khi x = 4
d) \(D = (x-1)(x+2)(x+3)(x+6)\)
\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)
\(=\left(x^2+5x\right)^2-36\ge-36\)
Vậy Dmin = - 36 khi \(\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)
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