\(^2\) - 4 ) = 0
b) x ( x - 2 ) - x + 2 = 0
c) x
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a) Ta có: \(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)

\(\Leftrightarrow\frac{\left(2x+1\right)^2\cdot3}{15}-\frac{5\left(x-1\right)^2}{15}-\frac{7x^2-14x-5}{15}=0\)

\(\Leftrightarrow3\left(4x^2+4x+1\right)-5\left(x^2-2x+1\right)-7x^2+14x+5=0\)

\(\Leftrightarrow12x^2+12x+3-5x^2+10x-5-7x^2+14x+5=0\)

\(\Leftrightarrow36x+3=0\)

\(\Leftrightarrow36x=-3\)

\(\Leftrightarrow x=\frac{-3}{36}\)

Vậy: \(x=\frac{-3}{36}\)

b) Ta có: \(\frac{201-x}{99}+\frac{203-x}{97}=\frac{205-x}{95}+3=0\)

\(\Leftrightarrow\frac{201-x}{99}+\frac{203-x}{97}-\frac{205-x}{95}-3=0\)

\(\Leftrightarrow\left(\frac{201-x}{99}+1\right)+\left(\frac{203-x}{97}+1\right)+\left(\frac{205-x}{95}+1\right)=0\)

\(\Leftrightarrow\frac{201-x+99}{99}+\frac{203-x+97}{97}+\frac{205-x+95}{95}=0\)

\(\Leftrightarrow\frac{300-x}{99}+\frac{300-x}{97}+\frac{300-x}{95}=0\)

\(\Leftrightarrow\left(300-x\right)\left(\frac{1}{99}+\frac{1}{97}+\frac{1}{95}\right)=0\)

\(\frac{1}{99}+\frac{1}{97}+\frac{1}{95}\ne0\)

nên 300-x=0

\(\Leftrightarrow x=300\)

Vậy: x=300

c) Ta có: \(x^3+x^2+x+1=0\)

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

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

Ta có: \(x^2\ge0\forall x\)

\(\Rightarrow x^2+1\ge1\ne0\forall x\)(2)

Từ (1) và (2) suy ra x+1=0

hay x=-1

Vậy: x=-1

d) Ta có: \(\left(x-1\right)x\left(x+1\right)\left(x+2\right)=24\)

\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)=24\)

Đặt \(x^2+x-1=t\)

\(\Leftrightarrow\left(t+1\right)\left(t-1\right)=24\)

\(\Leftrightarrow t^2-1-24=0\)

\(\Leftrightarrow t^2-25=0\)

\(\Leftrightarrow\left(t-5\right)\left(t+5\right)=0\)

\(\Leftrightarrow\left(x^2+x-1-5\right)\left(x^2+x-1+5\right)=0\)

\(\Leftrightarrow\left(x^2+x-6\right)\left(x^2+x+4\right)=0\)

\(\Leftrightarrow\left(x^2+3x-2x-6\right)\left(x^2+2\cdot x\cdot\frac{1}{2}+\frac{1}{4}+\frac{15}{4}\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x-2\right)\left[\left(x+\frac{1}{2}\right)^2+\frac{15}{4}=0\right]\)(3)

Ta có: \(\left(x+\frac{1}{2}\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+\frac{1}{2}\right)^2+\frac{15}{4}\ge\frac{15}{4}\ne0\forall x\)(4)

Từ (3) và (4) suy ra

\(\left[{}\begin{matrix}x+3=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=2\end{matrix}\right.\)

Vậy: \(x\in\left\{-3;2\right\}\)

e) Ta có: \(\left(5x-3\right)-\left(4x-7\right)=0\)

\(\Leftrightarrow5x-3-4x+7=0\)

\(\Leftrightarrow x+4=0\)

\(\Leftrightarrow x=-4\)

Vậy: x=-4

f) Ta có: \(3x^2+2x-1=0\)

\(\Leftrightarrow3x^2+3x-x-1=0\)

\(\Leftrightarrow3x\left(x+1\right)-\left(x+1\right)=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\3x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\frac{1}{3}\end{matrix}\right.\)

Vậy: \(x\in\left\{-1;\frac{1}{3}\right\}\)

g) Ta có: \(x^2+6x-16=0\)

\(\Leftrightarrow x^2-2x+8x-16=0\)

\(\Leftrightarrow x\left(x-2\right)+8\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+8\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-8\end{matrix}\right.\)

Vậy: \(x\in\left\{2;-8\right\}\)

h) Ta có: \(x^2+3x-10=0\)

\(\Leftrightarrow x^2+5x-2x-10=0\)

\(\Leftrightarrow x\left(x+5\right)-2\left(x+5\right)=0\)

\(\Leftrightarrow\left(x+5\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=2\end{matrix}\right.\)

Vậy: \(x\in\left\{-5;2\right\}\)

i) Ta có: \(x^2+x-2=0\)

\(\Leftrightarrow x^2-x+2x-2=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-2\end{matrix}\right.\)

Vậy: \(x\in\left\{1;-2\right\}\)

k) Ta có: \(3x^2+7x+2=0\)

\(\Leftrightarrow3x^2+6x+x+2=0\)

\(\Leftrightarrow3x\left(x+2\right)+\left(x+2\right)=0\)

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

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

Vậy: \(x\in\left\{-2;\frac{-1}{3}\right\}\)

l) Ta có: \(4x^2-12x+5=0\)

\(\Leftrightarrow4x^2-2x-10x+5=0\)

\(\Leftrightarrow2x\left(2x-1\right)-5\left(2x-1\right)=0\)

\(\Leftrightarrow\left(2x-1\right)\left(2x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\2x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=1\\2x=5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{1}{2}\\x=\frac{5}{2}\end{matrix}\right.\)

Vậy: \(x\in\left\{\frac{1}{2};\frac{5}{2}\right\}\)

25 tháng 6 2019

Tìm x,biết:

a/ x + 5x2 =0

⇔x ( 1 + 5x ) = 0

\(\Leftrightarrow\) x = 0 hoặc 1 + 5x = 0

1) x = 0

2) 1+ 5x = 0 \(\Leftrightarrow\) x = \(\frac{-1}{5}\)

Vậy: S = \(\left\{0;\frac{-1}{5}\right\}\)

b/x+1=(x+1)2

\(\Leftrightarrow\) (x+1) - (x+1)2 = 0

\(\Leftrightarrow\) ( x+ 1)(1-x-1) = 0

\(\Leftrightarrow\) (x+1).(-x) = 0

\(\Leftrightarrow\) x+1 = 0 hoặc x = 0

\(\Leftrightarrow\) x= -1 ; 0

Vậy: S=\(\left\{-1;0\right\}\)

c/ x3+x=0

\(\Leftrightarrow\) x(x2 + 1) = 0

\(\Leftrightarrow\) x = 0 hoặc x2 + 1 = 0

Ta có : x2 + 1 \(\ge\) 0 vs mọi x

Vậy: S = \(\left\{0\right\}\)


d/5x(x2)(2x)=0

\(\Leftrightarrow\) 5x(x-2) + (x - 2) = 0

\(\Leftrightarrow\) (x - 2)(5x+1) = 0

\(\Leftrightarrow\) x - 2 = 0 hoặc 5x+ 1 = 0

\(\Leftrightarrow\) x = 2 hoặc x = \(\frac{-1}{5}\)

Vậy: S = \(\left\{\frac{-1}{5};2\right\}\)

g/ x(x4)+(x4)2=0

⇔ (x - 4)( x+x-4) = 0

\(\Leftrightarrow\) x - 4 = 0 hoặc 2x-4=0

\(\Leftrightarrow\) x = 4 hoặc x = 2

Vậy: S= \(\left\{2;4\right\}\)

h/ x23x=0

⇔x (x-3) = 0

\(\Leftrightarrow\) x = 0 hoặc x = 3

Vậy: S = \(\left\{0;3\right\}\)

Vậy: S= \(\left\{0;3\right\}\)
i/4x(x+1)=8(x+1)

4x(x+1)-8(x+1) = 0

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

\(\Leftrightarrow\) x+1 = 0 hoặc x - 2 = 0

\(\Leftrightarrow\) x= -1 hoặc x = 2

Vậy: S=\(\left\{-1;2\right\}\)

4 tháng 12 2018

a) \(\left(3x-5\right)\left(2x+3\right)-\left(2x-3\right)\left(3x+7\right)-2x\left(x-4\right)\)

\(=\left(6x^2-x-15\right)-\left(6x^2+5x-21\right)-\left(2x^2-8x\right)\)

\(=6x^2-x-15-6x^2-5x+21-2x^2+8x\)

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

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

b) \(\left(x^2+2\right)^2-\left(x+2\right)\left(x-2\right)\left(x^2+4\right)\)

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

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

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

\(=x^4+4x^2+4-x^4+16\)

\(=4x^2+20\)

\(=4\left(x^2+5\right)\)

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

\(=\left(4x^2-4xy+y^2\right)-2\left(x^2+6xy+9y^2\right)-\left(9x^2-1\right)\)

\(=4x^2-4xy+y^2-2x^2-16xy-18y^2-9x^2+1\)

\(=-7x^2-20xy-17y^2+1\)

d) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2-1\right)\)

\(=\left(x^6-3x^4+3x^2-1\right)-\left(x^6-1\right)\)

\(=x^6-3x^4+3x^2-1-x^6+1\)

\(=-3x^4+3x^2\)

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

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

e) \(\left(2x-1\right)^2-2\left(4x^2-1\right)+\left(2x+1\right)^2\)

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

\(=\left[\left(2x-1\right)-\left(2x+1\right)\right]^2\)

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

\(=\left(-2\right)^2=4\)

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

\(=\left(x-y+z\right)^2+2\left(x-y+z\right)\left(y-z\right)+\left(y-z\right)^2\)

\(=\left(x-y+z+y+z\right)^2\)

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

h) \(\left(2x+3\right)^2+\left(2x+5\right)^2-\left(4x+6\right)\left(2x+5\right)\)

\(=\left(2x+3\right)^2-2\left(2x+3\right)\left(2x+5\right)+\left(2x+5\right)^2\)

\(=\left[\left(2x+3\right)-\left(2x+5\right)\right]^2\)

\(=\left(2x+3-2x-5\right)^2\)

\(=\left(-2\right)^2=4\)

i) \(5x^2-\dfrac{10x^3+15x^2-5x}{-5x}-3\left(x+1\right)\)

\(=5x^2-\dfrac{-5x\left(-2x^2-3x+1\right)}{-5x}-3\left(x+1\right)\)

\(=5x^2-\left(-2x^2-3x+1\right)-3\left(x+1\right)\)

\(=5x^2+2x^2+3x-1-3x-3\)

\(=7x^2-4\)

14 tháng 5 2019

casio fx 570vn

a: \(\Leftrightarrow x^2\left(x^2+x-12\right)=0\)

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

hay \(x\in\left\{0;-4;3\right\}\)

d: \(\left(x^2+5x\right)^2-2\left(x^2+5x\right)-24=0\)

\(\Leftrightarrow\left(x^2+5x-6\right)\left(x^2+5x+4\right)=0\)

\(\Leftrightarrow\left(x+6\right)\left(x-1\right)\left(x+1\right)\left(x+4\right)=0\)

hay \(x\in\left\{-6;1;-1;-4\right\}\)

f: \(x\left(x+1\right)\left(x-1\right)\left(x+2\right)=24\)

\(\Leftrightarrow\left(x^2+x\right)\left(x^2+x-2\right)=24\)

\(\Leftrightarrow\left(x^2+x\right)^2-2\left(x^2+x\right)-24=0\)

\(\Leftrightarrow x^2+x-6=0\)

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

hay \(x\in\left\{-3;2\right\}\)

18 tháng 8 2020

1) x2 - 7x =  0

=> x(x - 7) = 0

=> \(\orbr{\begin{cases}x=0\\x=7\end{cases}}\)

2) -3x2 + 5x = 0

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

=> \(\orbr{\begin{cases}x=0\\-3x+5=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\frac{5}{3}\end{cases}}\)

3) x2 - 19x - 20 = 0

=> x2 - 20x + x - 20 = 0

=> x(x - 20) + (x - 20) = 0

=> (x + 1)(x - 20) = 0

=> \(\orbr{\begin{cases}x+1=0\\x-20=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-1\\x=20\end{cases}}\)

4) x2 - 5x - 24 = 0

=> x2 - 8x + 3x - 24 = 0

=> x(x - 8) + 3(x - 8) = 0

=> (x + 3)(x - 8) = 0

=> \(\orbr{\begin{cases}x+3=0\\x-8=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-3\\x=8\end{cases}}\)

20 tháng 8 2020

1) x2 - 7x = 0

<=> x( x - 7 ) = 0

<=> \(\orbr{\begin{cases}x=0\\x=7\end{cases}}\)

2) -3x2 + 5x = 0

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

<=> \(\orbr{\begin{cases}x=0\\x=\frac{5}{3}\end{cases}}\)

3) x2 - 19x - 20 = 0

<=> x2 + x - 20x - 20 = 0

<=> x( x + 1 ) - 20( x + 1 ) = 0

<=> ( x - 20 )( x + 1 ) = 0

<=> \(\orbr{\begin{cases}x=20\\x=-1\end{cases}}\)

4) x2 - 5x - 24 = 0

<=> x2 + 3x - 8x - 24 = 0

<=> x( x + 3 ) - 8( x + 3 ) = 0

<=> ( x - 8 )( x + 3 ) = 0

<=> \(\orbr{\begin{cases}x=8\\x=-3\end{cases}}\)

16 tháng 9 2018

e, (x-1)(x2 + x + 1)-x(x+2)(x-2) = 5

x(x2 +x + 1 ) - (x2 + x +1 )- [ x (x2 - 4)] = 5

x3 +x2 +x - x2 - x - 1 - x3 +4x = 5

4x - 1 = 5

4x = 6

x =\(\dfrac{3}{2}\)

f, (x-1)3 - (x+3)(x2 - 3x +9 ) +3(x2 - 4) = 2

x - 3x2 +3x - 1 - [( x3 - 3x2 + 9x) + (3x2 - 9x +27)] = 2

x3 - 3x2 + 3x - 1 -x3 +3x2 -9x - 3x2 +9x - 27 +3x2 - 12 = 2

3x - 1 - 27 - 12 = 2

3x = 42

x = 14

16 tháng 9 2018

muốn tao trả lờ cho ko , mai đến lớp nhá

30 tháng 3 2018

Hỏi đáp Toán

30 tháng 3 2018

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