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25 tháng 11 2016
a)\(6x^2+5x-6=0\)
\(\Leftrightarrow6x^2-4x+9x-6=0\)
\(\Leftrightarrow2x\left(3x-2\right)+3\left(3x-2\right)=0\)
\(\Leftrightarrow\left(2x+3\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x+3=0\\3x-2=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-\frac{3}{2}\\x=\frac{2}{3}\end{array}\right.\)
b)\(6x^2-13x+6=0\)
\(\Leftrightarrow6x^2-4x-9x+6=0\)
\(\Leftrightarrow2x\left(3x-2\right)-3\left(3x-2\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(3x-2\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x-3=0\\3x-2=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{3}{2}\\x=\frac{2}{3}\end{array}\right.\)
c)\(10x^2-13x-3=0\)
\(\Leftrightarrow10x^2-15x+2x-3=0\)
\(\Leftrightarrow5x\left(2x-3\right)+\left(2x-3\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(5x+1\right)=0\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}2x-3=0\\5x+1=0\end{array}\right.\)\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{3}{2}\\x=-\frac{1}{5}\end{array}\right.\)
d)\(20x^2+19x-3=0\)
\(\Delta=19^2-\left(-4\left(20.3\right)\right)=601\)
\(\Rightarrow x_{1,2}=\frac{-19\pm\sqrt{601}}{40}\)
e)\(3x^2-x+6=0\)
\(\Delta=\left(-1\right)^2-4\left(3.6\right)=-71< 0\)
Suy ra vô nghiệm
VM
4
30 tháng 5 2018
a) 4x3 - 13x2 + 9x - 18
= 4x3 - 12x2 - x2 + 3x + 6x - 18
= 4x2( x - 3) - x( x - 3) + 6( x - 3)
= ( x - 3)( 4x2 - x + 6)
b) - x3 - 6x2 + 6x + 1
= 6x( 1 - x) + 1 - x3
= 6x( 1 - x) + ( 1 - x )( x2 + x + 1)
= ( 1 - x)( x2 + 7x + 1)
c) x3 + 3x2 + 3x + 2
= x3 + 2x2 + x2 + 2x + x + 2
= x2( x + 2) + x( x + 2) + x + 2
= ( x + 2)( x2 + x + 1)
30 tháng 5 2018
a) \(4x^3-13x^2+9x-18\)
\(=4x^3-12x^2-x^2+3x+6x-18\)
\(=4x^2\left(x-3\right)-x\left(x-3\right)+6\left(x-3\right)\)
\(=\left(x-3\right)\left(4x^2-x+6\right)\)
MA
29 tháng 6 2016
1. \(< =>\left(6x^2+31x+18\right)-\left(6x^2+13x+2\right)=x+1-a+6\)
\(< =>6x^2+31x+18-6x^2-13x-2=7\)
\(< =>18x+16=7\)
\(< =>18x=7-16\)
\(< =>18x=-9\)
\(< =>x=-\frac{9}{18}=-\frac{1}{2}\)
5 tháng 10 2017
\(x^3+6x^2-13x-42\)
\(=x^2\left(x+7\right)-x\left(x+7\right)-6\left(x+7\right)\)
\(=\left(x^2-x-6\right)\left(x+7\right)\)
\(=\left(x-3\right)\left(x+2\right)\left(x+7\right)\)
AT
30 tháng 6 2017
a, \(x^2-x-14x+14=0\)
\(=>x\left(x-1\right)-14\left(x-1\right)=0\)
\(=>\left(x-14\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-14=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=14\\x=1\end{matrix}\right.\)
b, \(x^2+2x+7x+14=0\)
\(=>x\left(x+2\right)+7\left(x+2\right)=0\)
\(=>\left(x+7\right)\left(x+2\right)=0\)
\(< =>\left\{{}\begin{matrix}x+7=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-7\\x=-2\end{matrix}\right.\)
c, \(6x^2-6x-5x+5=0\)
\(=>6x\left(x-1\right)-5\left(x-1\right)=0\)
\(=>\left(6x-5\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x-5=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{6}\\x=1\end{matrix}\right.\)
d, \(6x^2+3x+10x+5=0\)
\(=>3x\left(2x+1\right)+5\left(2x+1\right)=0\)
\(=>\left(3x+5\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x+5=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-5}{3}\\x=\dfrac{-1}{2}\end{matrix}\right.\)
e, \(10x^2+10x+3x+3=0\)
\(=>10x\left(x+1\right)+3\left(x+1\right)=0\)
\(=>\left(10x+3\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}10x+3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{-3}{10}\\x=-1\end{matrix}\right.\)
CHÚC BẠN HỌC TỐT...
1 tháng 12 2016
S(x) = x^9(x - 12) -x^8(x - 12) + x^7(x - 12) + . . . +x(x-12) - (x - 12) - 2
Suy ra: S(x) = -2
6 tháng 7 2018
\(1.6x\left(x-10\right)-2x+20=0\)
⇔\(6x\left(x-10\right)-2\left(x-10\right)=0\)
⇔ \(2\left(x-10\right)\left(3x-1\right)=0\)
⇔ x = 10 hoặc x = \(\dfrac{1}{3}\)
KL....
\(2.3x^2\left(x-3\right)+3\left(3-x\right)=0\)
⇔ \(3\left(x-3\right)\left(x^2-1\right)=0\)
⇔ \(x=+-1\) hoặc \(x=3\)
KL....
\(3.x^2-8x+16=2\left(x-4\right)\)
⇔ \(\left(x-4\right)^2-2\left(x-4\right)=0\)
⇔ \(\left(x-4\right)\left(x-6\right)=0\)
⇔ \(x=4\) hoặc \(x=6\)
KL.....
\(4.x^2-16+7x\left(x+4\right)=0\)
\(\text{⇔}4\left(x+4\right)\left(2x-1\right)=0\)
⇔ \(x=-4hoacx=\dfrac{1}{2}\)
KL.....
\(5.x^2-13x-14=0\)
⇔ \(x^2+x-14x-14=0\)
\(\text{⇔}\left(x+1\right)\left(x-14\right)=0\)
\(\text{⇔}x=14hoacx=-1\)
KL......
Còn lại tương tự ( dài quá ~ )
15 tháng 2 2017
a) Gần giống cho nó giống luôn.
cần thêm (-x^3+2x^2-x) là giống
\(\left(x-1\right)^4+x^3-2x^2+x=\left(x-1\right)^4+x\left(x^2-2x+1\right)=\left(x-1\right)^4+x\left(x-1\right)^2\)
\(\left(x-1\right)^2\left[\left(x-1\right)^2+x\right]\)
\(\left[\begin{matrix}x-1=0\Rightarrow x=0\\\left(x-1\right)^2+x=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}=0\end{matrix}\right.\)
Nghiệm duy nhất: x=1
8 tháng 9 2022
b; \(=6\left(x^2-4y^2\right)=6\left(x-2y\right)\left(x+2y\right)\)
d: =(x-1)(x-4)
e: =(x+3)(x+5)
PT <=> \(x^2-19x+48=0\)
\(\left(x-16\right)\left(x-3\right)=0\)
TH1 : x = 16 ; TH2 : x = 3
\(x^2-6x+39+9-13x\)
\(=x^2-19x+48\)