a) Phương trình có nghiệm bằng 1 khi \(1+a-4-4=0\)

\(\Rightarrow a=7\)

b) Khi a = 7 thì phương trình trở thành \(x^3+7x^2-4x-4=0\)

\(\Leftrightarrow-x^3-7x^2+4x+4=0\)

\(\Leftrightarrow\left(-x^3-8x^2-4x\right)+\left(x^2+8x+4\right)=0\)

\(\Leftrightarrow-x\left(x^2+8x+4\right)+\left(x^2+8x+4\right)=0\)

\(\Leftrightarrow\left(1-x\right)\left(x^2+8x+4\right)=0\)

+) 1 - x = 0 thì x = 1

+) \(x^2+8x+4=0\)

\(\Leftrightarrow x^2+8x+16-12=0\Leftrightarrow\left(x+4\right)^2=12\)

\(\Leftrightarrow\orbr{\begin{cases}x+4=\sqrt{12}\\x+4=-\sqrt{12}\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=\sqrt{12}-4\\x=-\sqrt{12}-4\end{cases}}\)

Vậy phương trình có 3 nghiệm \(\left\{1;\pm\sqrt{12}-4\right\}\)

a) \(ĐKXĐ:x\ne\pm3\)

Với a = -3

\(\Leftrightarrow A=\frac{x-3}{-3-x}-\frac{x+3}{-3+x}=\frac{-3\left[3.\left(-3\right)+1\right]}{\left(-3\right)^2-x^2}\)

\(\Leftrightarrow\frac{3-x}{x+3}-\frac{x+3}{x-3}=\frac{24}{9-x^2}\)

\(\Leftrightarrow\frac{3-x}{x+3}-\frac{x+3}{x-3}+\frac{24}{x^2-9}=0\)

\(\Leftrightarrow\frac{-\left(x-3\right)^2-\left(x+3\right)^2+24}{x^2-9}=0\)

\(\Leftrightarrow-x^2+6x-9-x^2-6x-9+24=0\)

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

\(\Leftrightarrow x^2=3\)

\(\Leftrightarrow x=\pm\sqrt{3}\)(tm)

Vậy với \(a=-3\Leftrightarrow x\in\left\{\sqrt{3};-\sqrt{3}\right\}\)

b) \(ĐKXĐ:x\ne\pm1\)

Với a = 1

\(\Leftrightarrow A=\frac{x+1}{1-x}-\frac{x-1}{1+x}=\frac{3+1}{1-x^2}\)

\(\Leftrightarrow\frac{x+1}{1-x}-\frac{x-1}{1+x}+\frac{4}{x^2-1}=0\)

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

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

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

\(\Leftrightarrow x^2=1\)

\(\Leftrightarrow x=\pm1\)(ktm)

Vậy với \(a=1\Leftrightarrow x\in\varnothing\)

c) \(ĐKXĐ:a\ne\pm\frac{1}{2}\)

Thay \(x=\frac{1}{2}\)vào phương trình, ta đươc :

\(A=\frac{\frac{1}{2}+a}{a-\frac{1}{2}}-\frac{\frac{1}{2}-a}{a+\frac{1}{2}}=\frac{a\left(3a+1\right)}{a^2-\frac{1}{4}}\)

\(\Leftrightarrow\frac{a+\frac{1}{2}}{a-\frac{1}{2}}+\frac{a-\frac{1}{2}}{a+\frac{1}{2}}-\frac{3a^2+a}{a^2-\frac{1}{4}}=0\)

\(\Leftrightarrow\frac{\left(a+\frac{1}{2}\right)^2+\left(a-\frac{1}{2}\right)^2-3a^2-a}{a^2-\frac{1}{4}}=0\)

\(\Leftrightarrow a^2+a+\frac{1}{4}+a^2-a+\frac{1}{4}-3a^2-a=0\)

\(\Leftrightarrow-a^2-a+\frac{1}{2}=0\)

\(\Leftrightarrow a^2+a-\frac{1}{2}=0\)

\(\Leftrightarrow\left(a+\frac{1}{2}\right)^2-\frac{3}{4}=0\)

\(\Leftrightarrow\orbr{\begin{cases}a=\frac{\sqrt{3}}{2}-\frac{1}{2}=\frac{\sqrt{3}-1}{2}\\a=-\frac{\sqrt{3}}{2}-\frac{1}{2}=\frac{-\sqrt{3}-1}{2}\end{cases}}\)(TM)

 Vậy với \(x=\frac{1}{2}\Leftrightarrow a\in\left\{\frac{\sqrt{3}-1}{2};\frac{-\sqrt{3}-1}{2}\right\}\) 

\(\left(x+4\right)^2-4x=\left(x-3\right)\left(x+3\right)-11\)

\(\Leftrightarrow x^2+8x+16-4x=x^2-9-11\)

\(\Leftrightarrow\left(x^2-x^2\right)+4x+\left(16+9+11\right)=0\)

\(\Leftrightarrow4x=-36\)

\(\Leftrightarrow x=-9\)

Vậy \(x=-9\)

\(\Leftrightarrow x^2+8x+16-4x=x^2-9-11\)

\(\Leftrightarrow x^2-x^2+8x-4x=-9-11-16\)

\(\Leftrightarrow4x=-36\)

\(\Leftrightarrow x=-9\)

a) Ta có : 

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

\(\Leftrightarrow3x=3x+2\)

\(\Leftrightarrow0=2\) ( vô lí )

Do đó pt đã cho vô nghiệm

b) Ta có  \(\left|x\right|=-x^2-2\) (1)

Nhân xét : VT (1) : \(\left|x\right|\ge0\forall x\)

VP (1) : \(-x^2\le0\Leftrightarrow-x^2-2\le-2\forall x\)

Do đó : \(VT\ne VP\)

Vì vậy pt đã cho vô nghiệm

(x-1)²-9=0

( x-1)²= 0+9 

(x-1)²=9

( x-1)²= 3²

=> x-1= 3

x= 3+1

x= 4

Vậy.....

bài này k đến lớp 8 đâu

\(\left(\text{x-1}\right)^2-9=0\)

<=>\(\left(x-1\right)^2=9\)

<=>\(x-1=3\)

<=>x=4

(x-10)²-125=x(x-15)-5

(x−10)^2−125=x(x−15)−5

Step 1: Simplify both sides of the equation.

x^2−20x−25=x^2−15x−5

<=>x^2−20x−25−x^2=x^2−15x−5−x^2

−20x−25=−15x−5

<=>−20x−25+15x=−15x−5+15x

−5x−25=−5

<=>−5x−25+25=−5+25

−5x=20
\(\frac{-5x}{-5}=\frac{20}{-5}\)

=> x=-4

\(P=\frac{x+1}{2x}\Rightarrow Q=2P=\frac{2x+2}{2x}=1+\frac{2}{2x}\)

\(\Rightarrow Q=2P\in Z\Leftrightarrow1+\frac{2}{2x}\in Z\Leftrightarrow\frac{2}{2x}\in Z\)

\(\Leftrightarrow2x\inƯ\left(2\right)=\left\{-1;1;-2;2\right\}\)

\(\Leftrightarrow x\in\left\{-\frac{1}{2};\frac{1}{2};-1;1\right\}\)

Mà \(x\in Z\Rightarrow x\in\left\{-1;1\right\}\)

...

\(6x^2-7x^2-16x+m=0\)

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

Nếu pt có 1 nghiệm bằng 1 thì \(-1-16+m=0\Rightarrow m=17\)

Phương trình trở thành \(-x^2-16x+17=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+17\right)=0\)

Suy ra nghiệm còn lại của pt là -17

-4kx + 2 = k - 1

x = -3 

<=> 12k + 2 = k - 1

<=> 11k = - 3

<=> k = -3/11

Vs \(x=-3\)

\(-4kx+2=k-1\Rightarrow-4k.\left(-3\right)+2=k-1\)

\(12k+2=k-1\)

\(12k-k=-1-2\)

\(11k=-3\Leftrightarrow k=-\frac{3}{11}\)

a, \(5\left(m+3x\right)\left(x+1\right)-4\left(1+2x\right)=80\)

Phương trình nhận \(x=2\)làm nghiệm nên :

\(5\left(m+3.2\right)\left(2+1\right)-4\left(1+2.2\right)=80\)

\(\Leftrightarrow15m+90-20=80\)

\(\Leftrightarrow15m=80+20-90\)

\(\Leftrightarrow15m=10\Leftrightarrow m=1,5\)

....

b, \(3\left(2x+m\right)\left(3x+2\right)-2\left(3x+1\right)^2=43\)

Phương trình nhận \(x=1\)làm nghiệm nên :

\(3\left(2.1+m\right)\left(3.1+2\right)-2\left(3.1+1\right)^2=43\)

\(\Leftrightarrow30+15m-32=43\)

\(\Leftrightarrow15m=43+32-30\)

\(\Leftrightarrow15m=45\Leftrightarrow m=3\)

....

\(\frac{315-x}{101}+\frac{313-x}{103}+\frac{311-x}{105}+\frac{309-x}{107}+4=0\)

\(\Leftrightarrow\frac{315-x}{101}+1+\frac{313-x}{103}+1+\frac{311-x}{105}+1+\frac{309-x}{107}+1=0\)

\(\Leftrightarrow\frac{416-x}{101}+\frac{416-x}{103}+\frac{416-x}{105}+\frac{416-x}{107}=0\)

\(\Leftrightarrow\left(416-x\right)\left(\frac{1}{101}+\frac{1}{103}+\frac{1}{105}+\frac{1}{107}\right)=0\)

\(\Leftrightarrow416-x=0\)

\(\Leftrightarrow x=416\)

a) 5(m + 3x)(x + 1) - 4(1 + 2x) = 80

Phương trình có nghiệm x = 2:

5(m + 3.2)(2 + 1) - 4(1 + 2.2) = 80

<=> 5(m + 6).3 - 4.5 = 80

<=> 15(m + 6) - 4.5 = 80

<=> 15(m + 6) - 20 = 80

<=> 15(m + 6) = 80 + 20

<=> 15(m + 6) = 100

<=> m + 6 = 100 : 15

<=> m + 6 = 20/3

<=> m = 20/3 - 6

<=> m = 2/3

b) 3(2x + m)(3x + 2) - 2(3x + 1)² = 43

Phương trình có nghiệm x = 1:

3(2.1 + m)(3.1 + 2) - 2(3.1 + 1)² = 43

<=> 3(2 + m).5 - 2.16 = 43

<=> 15(2 + m) - 32 = 43

<=> 15(2 + m) = 43 + 32

<=> 15(2 + m) = 75

<=> 2 + m = 75 : 15

<=> 2 + m = 5

<=> m = 5 - 2

<=> m = 3