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Bài 5 : a, -11-2x-x2=-(x2+2x)-11
=-(x2+2x+1)-11+1
=-(x+1)2-10\(\le-10\)
Dấu = xảy ra khi : -(x+1)2=0
\(\Leftrightarrow\)x=-1
b,-x2-5x=-(x2+5x)=-(x2+2.\(\frac{5}{2}\)x+\(\frac{25}{4}\))+\(\frac{25}{4}\)
=-(x+\(\frac{5}{2}\))2+\(\frac{25}{4}\le\frac{25}{4}\)
Dấu = xảy ra khi : -(x+\(\frac{5}{2}\))2=0
\(\Leftrightarrow\)x=\(-\frac{5}{2}\)
c, 3x-x2-7
=-(x2-3x)-7
=-(x2-2.\(\frac{3}{2}\)x+\(\frac{9}{4}\))-7+\(\frac{9}{4}\)
=-(x-\(\frac{3}{2}\))2-\(\frac{19}{4}\le-\frac{19}{4}\)
Dấu = xảy ra khi : -(x-\(\frac{3}{2}\))2=0
\(\Leftrightarrow x=\frac{3}{2}\)
Bài 4: a, x2-10x+27
=(x2-10x)+27
=(x2-2.5x+25)+27-25
=(x-5)2+2\(\ge\)2
Dấu = xảy ra khi : (x-5)2=0
\(\Leftrightarrow x=5\)
b, 4x2-6x+31
=(4x2-6x)+31
=(4x2-2.2x\(\frac{3}{2}\)+\(\frac{9}{4}\))+31-\(\frac{9}{4}\)
=(2x-\(\frac{3}{2}\))2+\(\frac{115}{4}\ge\frac{115}{4}\)
Dấu = xảy ra khi : (2x-\(\frac{3}{2}\))2=0
\(\Leftrightarrow\)x=\(\frac{3}{4}\)
c,9x2-12x+11
=(9x2-12x)+11
=(9x2-2.3x.2+4)+11-4
=(3x-2)2+7\(\ge\)7
Dấu = xảy ra khi : (3x-2)2=0
\(\Leftrightarrow x=\frac{2}{3}\)
\(đat:A=x^2-10x+27=x^2-10+25+2=\left(x-5\right)^2+2\ge0+2=2\Rightarrow A_{min}=2.\)
Dâú "=" xayr ra khi:x=5
Bài 4
a, x2 - 10x + 27
= ( x2 - 10x + 25 ) + 2
= ( x - 5 )2 +2
ta có: ( x - 5 )2 ≥ 0
=> (x - 5 )2 + 2 ≥ 2
Vậy GTNN của bt bằng 2 <=> x = 5
c, 9x2 - 12x +11
= 9x2 - 12x +4 +7
= ( 3x - 2 )2 +7
Ta có ( 3x - 2 )2 ≥ 0
=> ( 3x - 2 )2 + 7 ≥ 7
Vậy GTNN của bt = 7 <=> x= \(\frac{2}{3}\)