(x²-2x+4)(x²+3x+4)=14x²
Bài 1:Rút gọn biểu thức
a.(x-2)(2x-1)-(2x-3)(x-1)-2
b. x(x+3y+1) -2y (x-1) - (y+x+1)x
Bài 2: Tìm x
a. (14x^3 + 12x^2 -14x) :2x = (x+2) (3x-4)
b. (4x - 5) (6x+1) - (8x+3) (3x-4) =15
Bài 1.
a)
\((x-2)(2x-1)-(2x-3)(x-1)-2\\=2x^2-x-4x+2-(2x^2-2x-3x+3)-2\\=2x^2-5x+2-(2x^2-5x+3)-2\\=2x^2-5x+2-2x^2+5x-3-2\\=(2x^2-2x^2)+(-5x+5x)+(2-3-2)\\=-3\)
b)
\(x(x+3y+1)-2y(x-1)-(y+x+1)x\\=x^2+3xy+x-2xy+2y-xy-x^2-x\\=(x^2-x^2)+(3xy-2xy-xy)+(x-x)+2y\\=2y\)
Bài 2.
a)
\((14x^3+12x^2-14x):2x=(x+2)(3x-4)\\\Leftrightarrow 14x^3:2x+12x^2:2x-14x:2x=3x^2-4x+6x-8\\ \Leftrightarrow 7x^2+6x-7=3x^2+2x-8\\\Leftrightarrow (7x^2-3x^2)+(6x-2x)+(-7+8)=0\\\Leftrightarrow 4x^2+4x+1=0\\\Leftrightarrow (2x)^2+2\cdot 2x\cdot 1+1^2=0\\\Leftrightarrow (2x+1)^2=0\\\Leftrightarrow 2x+1=0\\\Leftrightarrow 2x=-1\\\Leftrightarrow x=\frac{-1}2\)
b)
\((4x-5)(6x+1)-(8x+3)(3x-4)=15\\\Leftrightarrow 24x^2+4x-30x-5-(24x^2-32x+9x-12)=15\\\Leftrightarrow 24x^2-26x-5-(24x^2-23x-12)=15\\\Leftrightarrow 24x^2-26x-5-24x^2+23x+12=15\\\Leftrightarrow -3x+7=15\\\Leftrightarrow -3x=8\\\Leftrightarrow x=\frac{-8}3\\Toru\)
tìm x
a(14x^3+12x^2-14x):2x=(x+2)(3x-4)
b(4x−5)(6x+1)−(8x+3)(3x−4)=15
a: ĐKXD: x<>0
\(\dfrac{14x^3+12x^2-14x}{2x}=\left(x+2\right)\left(3x-4\right)\)
=>\(\dfrac{2x\left(7x^2+6x-7\right)}{2x}=\left(x+2\right)\left(3x-4\right)\)
=>\(7x^2+6x-7=3x^2-4x+6x-8\)
=>\(7x^2+6x-7=3x^2+2x-8\)
=>\(4x^2+4x+1=0\)
=>\(\left(2x+1\right)^2=0\)
=>2x+1=0
=>x=-1/2(nhận)
b: \(\left(4x-5\right)\left(6x+1\right)-\left(8x+3\right)\left(3x-4\right)=15\)
=>\(24x^2+4x-30x-5-\left(24x^2-32x+9x-12\right)=15\)
=>\(24x^2-26x-5-24x^2+23x+12=15\)
=>-3x+7=15
=>-3x=8
=>\(x=-\dfrac{8}{3}\)
a, 3x(7x-2)-14x+4=0 b,2x+1/x-3 + 5-3x/x = 2x^2 -15 / x^2 -3x
a) Ta có: \(3x\left(7x-2\right)-14x+4=0\)
\(\Leftrightarrow3x\left(7x-2\right)-2\left(7x-2\right)=0\)
\(\Leftrightarrow\left(7x-2\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}7x-2=0\\3x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}7x=2\\3x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{7}\\x=\dfrac{2}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{2}{7};\dfrac{2}{3}\right\}\)
b) ĐKXĐ: \(x\notin\left\{0;3\right\}\)
Ta có: \(\dfrac{2x+1}{x-3}+\dfrac{5-3x}{x}=\dfrac{2x^2-15}{x^2-3x}\)
\(\Leftrightarrow\dfrac{x\left(2x+1\right)}{x\left(x-3\right)}+\dfrac{\left(5-3x\right)\left(x-3\right)}{x\left(x-3\right)}=\dfrac{2x^2-15}{x\left(x-3\right)}\)
Suy ra: \(2x^2+x+5x-15-3x^2+9x-2x^2+15=0\)
\(\Leftrightarrow-3x^2+15x=0\)
\(\Leftrightarrow-3x\left(x-5\right)=0\)
mà -3<0
nên x(x-5)=0
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=5\left(nhận\right)\end{matrix}\right.\)
Vậy: S={5}
1:
1). 2x-3=11-5x
2). 0,5(2x-9)=1,5x(x-5)
3). 28(x-1)-9(x-2)=14x
4). 8(3x-2)-14x=2(4-7x)+18x
5). 2(x-5)-6(1-2x)=3x+2
6). 2x-3=3(x-1)+x+2
1)2x-3=11-5x
2x+5x=11+3
7x =14
x=2.
thực hiện phép chia và tìm x để số dư bằng 0
a)(x^3-x^2-14x+24):(x^3+x-12)
b)(x^5+4x^3+3x^2-5x+15);(x^3-x+3)
c)(2x^4+2^3+3x^2-5x-20):(x^2+x+4)
d)(2x^4-14x^3+19x^2-20x+9):(x^2-4x+1)
giúp mk gấp vs ah!!!!!!
Phân tích đa thức thành nhân tử
( x² - 2x + 4 ) ( x² + 3x + 4 ) -14x²
Tìm x biết
( x2 - 2x + 4 )( x2 + 3x + 4 ) = 14x2
\(\left(x^2-2x+4\right)\left(x^2+3x+4\right)=14x^2\)
\(\Leftrightarrow x^4+3x^3+4x^2-2x^3-6x^2-8x+4x^2+12x+16=14x^2\)
\(\Leftrightarrow x^4+x^3+2x^2-14x^2+4x=0\)
\(\Leftrightarrow x^4+x^3-12x^2+4x=0\)
\(\Leftrightarrow x\left(x^3+x^2-12x+4\right)=0\)
\(\Leftrightarrow x=0\) ( vì \(x^3+x^2-12x+4\ne0\) )
1).(4-3x)(10-5x)=0 2).(7-2x)(4+8x)=0 3).(9-7x)(11-3x)=0
4).(7-14x)(x-2)=0 5).(\(\dfrac{7}{8}\)-2x)(3x+\(\dfrac{1}{3}\))=0 6).3x-2x\(^2\)
7).5x+10x\(^2\)
1.
<=> \(\left[{}\begin{matrix}4-3x=0\\10-5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=2\end{matrix}\right.\)
2.
<=>\(\left[{}\begin{matrix}7-2x=0\\4+8x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
3.
<=>\(\left[{}\begin{matrix}9-7x=0\\11-3x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{7}\\x=\dfrac{11}{3}\end{matrix}\right.\)
4.
<=>\(\left[{}\begin{matrix}7-14x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=2\end{matrix}\right.\)
5.
<=>\(\left[{}\begin{matrix}\dfrac{7}{8}-2x=0\\3x+\dfrac{1}{3}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{16}\\x=-\dfrac{1}{9}\end{matrix}\right.\)
6,7. ko đủ điều kiện tìm
Giải phương trình sau đây :
a ) 8 ( 3 x - 2 ) - 14 x = 2 ( 4 – 7 x ) + 15 x b ) ( 3 x – 1 ) ( x – 3 ) – 9 + x 2 = 0 c ) | x - 2 | = 2 x - 3 d ) x + 2 x - 2 - 1 x = 2 x x - 2
a) 8( 3x - 2 ) - 14x = 2( 4 – 7x ) + 15x
⇔ 24x – 16 -14x = 8 – 14x + 15x
⇔ 10x -16 = 8 + x
⇔ 9x = 24
⇔ x = 24/9
b) ( 3x – 1 )( x – 3 ) – 9 + x2 = 0
⇔ (3x -1)( x – 3) + (x - 3)( x + 3) = 0
⇔ (x - 3)(3x - 1 + x - 3) = 0
⇔ (x - 3)(4x - 4) = 0
c) |x - 2| = 2x - 3
TH1: x - 2 ≥ 0 ⇔ x ≥ 2
Khi đó: x - 2 = 2x – 3
⇔ 2x – x = -2 + 3
⇔ x = 1 (không TM điều kiện x ≥ 2)
TH2: x – 2 < 0 ⇔ x < 2
Khi đó: x-2 = -(2x – 3)
⇔ x – 2 = -2x + 3
⇔ 3x = 5
⇔ x = 5/3 ( TM điều kiện x < 2)
MTC: x(x-2)
ĐKXĐ: x ≠ 0;x ≠ 2
Đối chiếu với ĐKXĐ thì pt có nghiệm x = - 1