Tìm x :
8x - 6 = 18
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a) Ta có: \(A=x^2-2x+5=\left(x^2-2x+1\right)+4\)
\(A=\left[x^2-2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2+\frac{3}{4}\right]+4\)
\(A=\left(x-\frac{1}{2}\right)^2+\frac{1}{4}+4=\left(x-\frac{1}{2}\right)^2+\frac{17}{4}\ge\frac{17}{4}\)
=>AMin=17/4
Dấu "=" xảy ra <=> x=1/2
b,\(E=-x^2+2x-3=-\left(x^2-2x+3\right)\)
Đặt \(M=x^2-2x+3\).dễ thấy E=-M
ta có: \(M=\left(x^2-2x+1\right)+2=\left(x^2-2.x.\frac{1}{2}+\left(\frac{1}{2}\right)^2+\frac{3}{4}\right)+2=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}+2\)
\(M=\left(x-\frac{1}{2}\right)^2+\frac{11}{4}\ge\frac{11}{4}\)
Mà E=-M
=>\(E\le\frac{11}{4}\)
=>EMax=11/4
Dấu "=" xảy ra <=>x=1/2
b: \(B=\sqrt{x^2-8x+18}-1\)
\(=\sqrt{\left(x-4\right)^2+2}-1\)
(x-4)^2+2>=2
=>\(\sqrt{\left(x-4\right)^2+2}>=\sqrt{2}\)
=>B>=căn 2-1
Dấu = xảy ra khi x=4
a: \(D=3+\sqrt{2x^2-8x+33}\)
\(=3+\sqrt{2\left(x^2-4x+\dfrac{33}{2}\right)}\)
\(=\sqrt{2\left(x^2-4x+4\right)+25}+3\)
\(=\sqrt{2\left(x-2\right)^2+25}+3>=5+3=8\)
Dấu = xảy ra khi x=2
`4|8x-3|+5|3-2x|=18`
`<=>4|8x-3|+5|2x-3|=18`
Nếu `x>=3/2=>|8x-3|=8x-3,|2x-3|=2x-3`
`pt<=>4(8x-3)+5(2x-3)=18`
`<=>32x-12+10x-15=18`
`<=>42x=27+18=45`
`<=>x=45/42(l)`
Nếu `x<=3/8=>|8x-3|=3-8x,|2x-3|=3-2x`
`pt<=>4(3-8x)+5(3-2x)=18`
`<=>12-32x+15-10x=18`
`<=>27-42x=18`
`<=>9=42x`
`<=>x=3/14(tm)`
Nếu `3/9<=x<=3/2=>|8x-3|=8x-3,|2x-3|=3-2x`
`pt<=>4(8x-3)+5(3-2x)=18`
`<=>32x-12+15-10x=18`
`<=>22x+3=18`
`<=>22x=15`
`<=>x=15/22(tm)`
Vậy x=15/22 hoặc x=3/14
18 . [(8x + 10 ) : 5] + 12 = 490
18 . [(8x + 10 ) : 5] = 490 - 12
18 . [(8x + 10 ) : 5] = 478
[(8x + 10 ) : 5] = 478 : 18
( 8x + 10 ) : 5 = \(\frac{239}{9}\)
8x + 10 = \(\frac{239}{9}\) .5
8x + 10 = \(\frac{1195}{9}\)
8x = \(\frac{1195}{9}\) - 10
8x = \(\frac{1195}{9}-\frac{90}{9}\)
8x = \(\frac{1105}{9}\)
x = \(\frac{1105}{9}\)\(\div\)8
x = \(\frac{1105}{9}\) . \(\frac{1}{8}\)
x = \(\frac{1105}{72}\)
\(A=\dfrac{4\left(x^2+2x+3-3\right)+18}{x^2+2x+3}=\dfrac{4\left(x^2+2x+3\right)+6}{x^2+2x+3}=4+\dfrac{6}{\left(x+1\right)^2+2}\)
Ta có \(\left(x+1\right)^2+2\ge2\Rightarrow\dfrac{6}{\left(x+1\right)^2+2}\le3\Leftrightarrow4+\dfrac{6}{\left(x+1\right)^2+2}\le7\)
Dấu ''='' xảy ra khi x = -1
8x - 6 = 18
8x = 18 + 6
8x = 24
x = 24 : 8
x = 3
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