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Bài 4:

a: \(2x^4+18x^2=0\)

=>\(2x^2\left(x^2+9\right)=0\)

=>\(x^2=0\) (Vì \(2\left(x^2+9\right)=2x^2+18\ge18>0\forall x\) )

=>x=0

b: (x-5)(x+5)-15x+75=0

=>(x-5)(x+5)-15(x-5)=0

=>(x-5)(x+5-15)=0

=>(x-5)(x-10)=0

=>\(\left[\begin{array}{l}x-5=0\\ x-10=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\\ x=10\end{array}\right.\)

c: \(x^4=x^2\)

=>\(x^4-x^2=0\)

=>\(x^2\left(x^2-1\right)=0\)

=>\(\left[\begin{array}{l}x^2=0\\ x^2-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x^2=0\\ x^2=1\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=1\\ x=-1\end{array}\right.\)

d: \(12x\left(6x-1\right)-24x^2=0\)

=>12x(6x-1-2x)=0

=>x(4x-1)=0

=>\(\left[\begin{array}{l}x=0\\ 4x-1=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=\frac14\end{array}\right.\)

Bài 2:

a: 4x-16+3y(4-x)

=4(x-4)-3y(x-4)

=(x-4)(4-3y)

b: \(9y^2-6y+1=\left(3y\right)^2-2\cdot3y\cdot1+1^2=\left(3y-1\right)^2\)

c: \(25x^2-4=\left(5x\right)^2-2^2=\left(5x-2\right)\left(5x+2\right)\)

d: \(x^2-12x+36=x^2-2\cdot x\cdot6+6^2=\left(x-6\right)^2\)

e: \(8x^3+36x^2+54x+27\)

\(=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2+3^3\)

\(=\left(2x+3\right)^3\)

f: \(\left(2x-5\right)^2-\left(2x+y\right)^2\)

=(2x-5-2x-y)(2x-5+2x+y)

=(-y-5)(4x+y-5)

g: \(\left(2x-y\right)^3+\left(2x+y\right)^3\)

\(=8x^3-12x^2y+6xy^2-y^3+8x^3+12x^2y+6xy^2+y^3\)

\(=16x^3+12xy^2=4x\left(4x^2+3y^2\right)\)

Câu 1:

a: \(6x^2-72x=0\)

=>\(6\left(x^2-12x\right)=0\)

=>\(x^2-12x=0\)

=>x(x-12)=0

=>\(\left[\begin{array}{l}x=0\\ x-12=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=12\end{array}\right.\)

b: \(-2x^4+16x=0\)

=>\(-2x\left(x^3-8\right)=0\)

=>\(x\left(x^3-8\right)=0\)

=>\(\left[\begin{array}{l}x=0\\ x^3-8=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x^3=8\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=2\end{array}\right.\)

c: \(\left(2x-1\right)^3-8x\left(x-3\right)\cdot\left(x+3\right)=-1\)

=>\(8x^3-12x^2+6x-1-8x\cdot\left(x^2-9\right)=-1\)

=>\(8x^3-12x^2+6x-1-8x^3+72x=-1\)

=>\(-12x^2+78x=0\)

=>-6x(2x-13)=0

=>x(2x-13)=0

=>\(\left[\begin{array}{l}x=0\\ 2x-13=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=\frac{13}{2}\end{array}\right.\)

d: \(x\left(x-5\right)-\left(x-3\right)^2=0\)

=>\(x^2-5x-\left(x^2-6x+9\right)=0\)

=>\(x^2-5x-x^2+6x-9=0\)

=>x-9=0

=>x=9

e: \(x\left(x-5\right)+3\left(x-5\right)=0\)

=>(x-5)(x+3)=0

=>\(\left[\begin{array}{l}x-5=0\\ x+3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\\ x=-3\end{array}\right.\)

f: 2x(x-8)-5(8-x)=0

=>2x(x-8)+5(x-8)=0

=>(x-8)(2x+5)=0

=>\(\left[\begin{array}{l}x-8=0\\ 2x+5=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=8\\ x=-\frac52\end{array}\right.\)

g: \(30x-15x^2=0\)

=>15x(2-x)=0

=>x(2-x)=0

=>\(\left[\begin{array}{l}x=0\\ 2-x=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=0\\ x=2\end{array}\right.\)

h: \(-4x^3-12x=0\)

=>\(-4x\left(x^2+3\right)=0\)

=>x=0

Tham khảo

x.x-2.x-1-y.y

\(\) \(x^2-2x-1-y^2=(x^2-2x+1)-2+y^2=(x-1)^2+y^2-2=((x-1)-y)((x-1)+y)-2=(x-1-y)(x+1+y)+2\)

a) ... \(\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+2\right)=0\Leftrightarrow\hept{\begin{cases}x=1\\x=2\\x=-2\end{cases}}\)Vậy.....

b) ... \(\Leftrightarrow x^3\left(x-2\right)+10x\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^3+10x\right)=0\)

\(\Leftrightarrow x\left(x-2\right)\left(x^2+10\right)=0\Leftrightarrow\hept{\begin{cases}x=0\\x=2\\x^2=-10\Rightarrow x\in\theta\end{cases}}\)(\(\theta\)là rỗng) Vậy.........

c) ... \(\Leftrightarrow2x-3=x+5\Leftrightarrow x=8\)Vậy.......

d) ... \(\Leftrightarrow x\left(x^2-16\right)=0\Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\Leftrightarrow\hept{\begin{cases}x=0\\x=4\\x=-4\end{cases}}\)Vậy......

\(a)\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}=\frac{-3}{4}\left(x\ne-3;x\ne2\right)\)

\(\Leftrightarrow\frac{x+2}{x+3}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{1}{x-2}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x^2-4}{\left(x-2\right)\left(x+3\right)}-\frac{5}{\left(x+3\right)\left(x-2\right)}-\frac{x+3}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x^2-4-5-x-3}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x^2-x-12}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{\left(x-4\right)\left(x+3\right)}{\left(x-2\right)\left(x+3\right)}=\frac{-3}{4}\)

\(\Leftrightarrow\frac{x-4}{x-2}=\frac{-3}{4}\)

<=> 4x-16=-3x+6

<=> 4x-16+3x-6=0

<=> 7x-22=0

<=> 7x=22

<=> \(x=\frac{22}{7}\)(TMĐK)
 

a)\(\Leftrightarrow3x^2-3x^2+6x=36\Leftrightarrow6x=36\Leftrightarrow x=6\)

1) \(\frac{x-3}{2}+\frac{4x+1}{3}=\frac{2x-7}{6}\)

<=> 3(x - 3) + 2(4x + 1) = 2x - 7

<=> 3x - 9 + 8x + 2 = 2x - 7

<=> 11x - 7 = 2x - 7

<=> 11x - 7 - 2x = -7

<=> 9x - 7 = -7

<=> 9x = -7 + 7

<=> 9x = 0

<=> x = 0

\(A=\left(x-4\right)^2-\left(x+4\right)^2-16\left(x-2\right)\)

\(=x^2-8x+16-x^2-8x-16-16x+32\)

\(=-32x+32\)

Biểu thức phụ thuộc vào giá trị của biến

b) \(\left(x-3\right)^3-\left(x+3\right)^3+12\left(x+1\right)\left(x-1\right)\)

\(=\left(x^3-9x^2+27x-27\right)-\left(x^3+9x^2+27x+27\right)+12x^2-12\)

\(=-6x^2-66\)

Biểu thức này phụ thuộc vào giá trị của biến

a)\(2x\left(x-2016\right)-2x+4032=0\)

\(\Leftrightarrow2x\left(x-2016\right)-2\left(x-2016\right)=0\)

\(\Leftrightarrow\left(2x-2\right)\left(x-2016\right)=0\)

\(\Leftrightarrow2\left(x-1\right)\left(x-2016\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x-1=0\\x-2016=0\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=1\\x=2016\end{array}\right.\)

b)\(5x\left(x-3\right)=x-3\)

\(\Leftrightarrow5x\left(x-3\right)-\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(5x-1\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x-3=0\\5x-1=0\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=3\\x=\frac{1}{5}\end{array}\right.\)

c)\(\left(3x-1\right)^2=\left(x+2\right)^2\)

\(\Leftrightarrow\left(3x-1\right)^2-\left(x+2\right)^2=0\)

\(\Leftrightarrow\left(3x-1+x+2\right)\left[\left(3x-1\right)-\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left(4x+1\right)\left(2x-3\right)=0\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}4x+1=0\\2x-3=0\end{array}\right.\)

\(\Leftrightarrow\left[\begin{array}{nghiempt}x=-\frac{1}{4}\\x=\frac{3}{2}\end{array}\right.\)

thank you very much !

a) \(\dfrac{2x-5}{3}-\dfrac{3x-1}{2}\)<\(\dfrac{3-x}{5}-\dfrac{2x-1}{4}\)

=> 20(2x-5)-30(3x-1)<12(3-x)-15(2x-1)

<=>40x-100-90x+30<36-12x-30x+15

<=>-50x-70<51-42x

<=>-50x+42x<51+70

<=> -8<121

<=>x>\(\dfrac{-121}{8}\)

=> S={x|x>\(\dfrac{-121}{8}\)}

b) 5x-\(\dfrac{3-2x}{2}\)>\(\dfrac{7x-5}{2}\)+x

=> 10x-(3-2x)>7x-5+2x

<=>10x-3+2x>7x-5+2x

<=>10x-3>7x-5

<=>10x-7x>-5+3

<=>3x>-2

<=>x>\(\dfrac{-2}{3}\)

=>S={x|x>\(\dfrac{-2}{3}\)}