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a, ( 8x - 3 ) ( 3x + 2 ) - ( 4x + 7 ) ( x + 4 ) = ( 2x + 1 ) ( 5x - 1 )
( 24x2 + 16x - 9x - 6 ) - ( 4x2 - 16x - 7x + 28 ) = 10x2 - 2x + 5x -1
24x2 + 16x - 9x - 6 -4x2 - 16x - 7x - 10x2 + 2x - 5x = 6 + 28 - 1
10x2 -19x = 33
10x2 - 19x -33 = 0 \(\Leftrightarrow\)10x( x+ 3 ) + 11 ( x- 3 ) = 0
=> ( x- 3 ) ( 10x + 11 ) = 0\(\Rightarrow\orbr{\begin{cases}x=3\\x=\frac{-11}{10}\end{cases}}\)
b, 4( x - 1 ) ( x + 5 ) - ( x + 2 ) ( x + 5 ) = 3( x - 1 ) ( x + 2 )
4( x2 - 5x - x + 5 ) - ( x2 + 5x + 2x + 10 ) = 3( x2 + 2x - x - 2 )
4x2 - 20x - 4x + 20 - x2 - 5x - 2x - 10 = 3x2 + 6x - 3x - 6
( 4x2 - x2 ) + ( -20x - 4x - 5x - 2x ) + 20 - 10 = 3x2 + ( 6x - 3x ) - 6
3x2 - 31x - 3x2 - 3x = -6-10
-34x = -16
x = \(\frac{8}{17}\)
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\(A=\left(-3x+1\right)^2-\frac{3}{4}\)
Vì:\(\left(-3x+1\right)^3\ge0\forall x\in R\)
\(\Rightarrow\left(-3x+1\right)^2-\frac{3}{4}\ge\frac{-3}{4}\forall x\in R\)
Dấu "="xảy ra<=> \(\left(-3x+1\right)^2=0\Leftrightarrow x=\frac{1}{3}\)
vậy Amin =\(\frac{-3}{4}\) tại x=\(\frac{1}{3}\)
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D = \(x^{10}-25x^9+25x^8-25x^7+...+25x^2-25x+25\)với x = 24
thiếu 1 câu
A= x5−5x4+5x3−5x2+5x−1x5−5x4+5x3−5x2+5x−1 với x = 4
= x5−(x+1)x4+(x+1)x3−(x+1)x2+(x+1)x−1
= x5−x5−x4+x4+x3−x3+x2−x2+x−1
=x−1=4−1=3
Tương tự với các câu B,C,D
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ta có: f(x) + g(x) = ( 7 x^6 - 6x ^5 +5x^4 -4x^3 +3x^2 -2x +1) - ( x - 2x^2 +3x^3 - 4x^4 + 5x^5 - 6x^6)
\(=7x^6-6x^5+5x^4-4x^3+3x^2-2x+1-x+2x^2-3x^3+4x^4-5x^5+6x^6\)
\(=\left(7x^6+6x^6\right)-\left(6x^5+5x^5\right)+\left(5x^4+4x^4\right)-\left(4x^3+3x^3\right)+\left(3x^2+2x^2\right)-\left(2x+x\right)+1\)
\(=13x^6-11x^5+9x^4-7x^3+5x^2-3x+1\)
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câu a tẹo mình chụp bài cho nhé
b) \(2\left|x-1\right|+3x=7\)
\(\Leftrightarrow2\left|x-1\right|=7-3x\left(1\right)\)
Vì \(2\left|x-1\right|\ge0;\forall x\)
\(\Rightarrow7-3x\ge0;\forall x\)
\(\Rightarrow x\le\frac{7}{3}\)
Từ \(\left(1\right)\Rightarrow\orbr{\begin{cases}2\left(x-1\right)=7-3x\\2\left(1-x\right)=7-3x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}2x-2=7-3x\\2-2x=7-3x\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}5x=9\\x=5\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=\frac{9}{5}\left(tm\right)\\x=5\left(loai\right)\end{cases}}\)
Vậy \(x=\frac{9}{5}\)
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a: \(\Leftrightarrow6x^2+2x+12x-6x^2=7\)
=>14x=7
hay x=1/2
b: \(\Leftrightarrow72-20x-36x+84=30x-240-6x-84\)
=>-56x+156=24x-324
=>-80x=-480
hay x=6
c: \(\Leftrightarrow6x^2+27x+4x+18-6x^2-x-12x-2=x+1-x+6=7\)
=>18x+16=7
=>18x=-9
hay x=-1/2
Giải:
\(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|=5x\)
\(\ge\left|x+1+x+2+x+3+x+4\right|=5x\)
\("="\Leftrightarrow\left|4x+10\right|=5x\)
\(\Leftrightarrow\left[{}\begin{matrix}4x+10=5x\\4x+10=-5x\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=10\left(n\right)\\x=-\dfrac{10}{9}\left(l\right)\end{matrix}\right.\)
Vậy ...
Ta có
\(\left|x+1\right|\ge0\)
\(\left|x+2\right|\ge0\)
\(\left|x+3\right|\ge0\)
\(\left|x+4\right|\ge0\)
=> \(\left|x+1\right|+\left|x+2\right|+\left|x+3\right|+\left|x+4\right|\ge0\)
=> 5x\(\ge0\)
Dấu "=" xảy ra <=>
x+1+x+2+x+3+x+4=5x
=> (x+x+x+x)+(1+2+3+4)=5x
=> 4x+10=5x
=> 5x-4x=10
=> x=10
Vậy x=10
cô giáo mk dạy vậy đó , nên chắc chắn là đúng