a: =>31-x=60

=>x=-29

b: =>(x-140):35=280-270=10

=>x-140=350

=>x=490

c: =>(1900-2x):35=48

=>1900-2x=1680

=>2x=220

=>x=110

d: =>\(2^{2x-1}=2^9\cdot2=2^{11}\)

=>2x-1=11

=>x=6

e: =>(x+2)^5=4^5

=>x+2=4

=>x=2

f: =>3x-4=0 hoặc x-1=0

=>x=4/3 hoặc x=1

g: =>(2x-1)^2=49

=>2x-1=7 hoặc 2x-1=-7

=>x=-3 hoặc x=4

h: =>x(x+1)/2=78

=>x(x+1)=156

=>x=12

1.\(\left(x+5\right)^2=x^2+10x+25\)

2. \(\left(2x-5y\right)^2=4x^2-20xy+25y^2\)

3. \(\left(x+8\right)\left(x-8\right)=x^2-64\)

4. \(\left(x+4\right)^3=x^3+12x^2+48x+64\)

5. \(\left(2x-1\right)^3=8x^3-12x^2+6x-1\)

1:

=>2x-3=0 hoặc 5/2-x=0

=>x=3/2 hoặc x=5/2

2: =>x=1/2+12=12,5

3: =>(2x+3/5-3/5)(2x+3/5+3/5)=0

=>2x(2x+6/5)=0

=>x=0 hoặc x=-3/5

4: =>-1/6x=-1/3

=>x=1/3:1/6=2

5: =>1/4:x=1/4

=>x=1

6: =>2/5x+11/15=1

=>2/5x=4/15

=>x=2/3

`1,[(-3).3+5]-26=-2x-3`

`=>(-9+5)-26=-2x-3`

`=>-4-26=-2x-3`

`=>-30=-2x-3`

`=>-2x=-27`

`=>x=27/2`

Vậy `x=27/2`

`2)-[(-35)-3]=2x-2`

`=>-(-38)=2x-2`

`=>38=2x-2`

`=>2x=40`

`=>x=20`

Vậy `x=20`

1) \(\left[\left(-3\right)\cdot3+5\right]-26=-2x-3\\ \Rightarrow-9+5-26=-2x-3\\ \Rightarrow-2x=-9+5-26+3\\ \Rightarrow-2x=-27\\ \Rightarrow x=\dfrac{27}{2}\)

Vậy \(x=\dfrac{27}{2}\)

2) \(-\left[\left(-35\right)-3\right]=2x-2\\ \Rightarrow2x-2=-\left(-38\right)\\ \Rightarrow2x=38+2\\ \Rightarrow2x=40\\ \Rightarrow x=20\)

Vậy \(x=20\)

1) Ta có: \(\left[\left(-3\right)\cdot3+5\right]-26=-2x-3\)

\(\Leftrightarrow-2x-3=-4-26\)

\(\Leftrightarrow-2x-3=-30\)

\(\Leftrightarrow-2x=-27\)

hay \(x=\dfrac{27}{2}\)

Vậy: \(x=\dfrac{27}{2}\)

2) Ta có: \(-\left[\left(-35\right)-3\right]=2x-2\)

\(\Leftrightarrow2x-2=-\left(-38\right)\)

\(\Leftrightarrow2x-2=38\)

\(\Leftrightarrow2x=40\)

hay x=20

Vậy: x=20

a: =>x-5=9

=>x=14

b: căn x-10=-2

=>\(x\in\varnothing\)

c: căn 2x-1=căn 5

=>2x-1=5

=>2x=6

=>x=3

d: căn 4-5x=12

=>4-5x=144

=>5x=-140

=>x=-28

e: =>7|x-1|=35

=>|x-1|=5

=>x-1=5 hoặc x-1=-5

=>x=6 hoặc x=-4

f: =>\(\sqrt{x+3}\left(\sqrt{x-3}-5\right)=0\)

=>x+3=0 hoặc x-3=25

=>x=28 hoặc x=-3

b.

ĐKXĐ: \(x\ge-1\)

\(\sqrt{\left(x+1\right)\left(x+35\right)}-14\sqrt{x+35}+84-6\sqrt{x+1}=0\)

\(\Leftrightarrow\sqrt{x+1}\left(\sqrt{x+35}-14\right)-6\left(\sqrt{x+35}-14\right)=0\)

\(\Leftrightarrow\left(\sqrt{x+1}-6\right)\left(\sqrt{x+35}-14\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+1}=6\\\sqrt{x+35}=14\end{matrix}\right.\)

\(\Leftrightarrow...\)

a. ĐKXĐ: \(-1\le x\le1\)

Đặt \(\left\{{}\begin{matrix}\sqrt{x+1}=a\ge0\\\sqrt{1-x}=b\ge0\end{matrix}\right.\)

\(\Rightarrow a+2a^2=-b^2+b+3ab\)

\(\Leftrightarrow\left(2a^2-3ab+b^2\right)+a-b=0\)

\(\Leftrightarrow\left(a-b\right)\left(2a-b\right)+a-b=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}a=b\\2a+1=b\end{matrix}\right.\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\4x+5+4\sqrt{x+1}=1-x\left(1\right)\end{matrix}\right.\)

(1) \(\Leftrightarrow4\sqrt{x+1}=-4-5x\) \(\left(x\le-\dfrac{4}{5}\right)\)

\(\Leftrightarrow16\left(x+1\right)=25x^2+40x+16\)

\(\Leftrightarrow25x^2+24x=0\Rightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=-\dfrac{24}{25}\end{matrix}\right.\)

c.

ĐKXĐ: \(x\ge-\dfrac{3}{2}\)

\(\Leftrightarrow x\sqrt{2x+3}-\sqrt{2x+3}+3-3x+3\sqrt{x+5}-\sqrt{\left(2x+3\right)\left(x+5\right)}=0\)

\(\Leftrightarrow\sqrt{2x+3}\left(x-1\right)-3\left(x-1\right)-\sqrt{x+5}\left(\sqrt{2x+3}-3\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(\sqrt{2x+3}-3\right)-\sqrt{x+5}\left(\sqrt{2x+3}-3\right)=0\)

\(\Leftrightarrow\left(x-1-\sqrt{x+5}\right)\left(\sqrt{2x+3}-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1-\sqrt{x+5}=0\\\sqrt{2x+3}-3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+5-\sqrt{x+5}-6=0\\\sqrt{2x+3}=3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x+5}=-2\left(loại\right)\\\sqrt{x+5}=3\\\sqrt{2x+3}=3\end{matrix}\right.\)

\(\Leftrightarrow...\)

b) Ta có: \(\left(x^2-7\right)\left(x+2\right)-\left(2x-1\right)\left(x-14\right)+x\left(x^2-2x-22\right)+35\)

\(=x^3+2x^2-7x-14-\left(2x^2-28x-x+14\right)+x^3-2x^2-22x+35\)

\(=2x^3-29x+21-2x^2+29x-14\)

\(=2x^3-2x^2+7\)

a.

$xy=-21=7.(-3)=(-7).3=3.(-7)=(-3).7=21.(-1)=(-21).1=(-1).21=1(-21)$

Do đó $(x,y)=(7,-3); (-7,3); (3,-7); (-3,7); (21,-1); (-21,1); (-1,21); (1,-21)$

b.

$(x+5)(y-3)=14=1.14=14.1=(-14)(-1)=(-1)(-14)=2.7=7.2=(-2)(-7)=(-7)(-2)$

Do đó:

$(x+5,y-3)=(1,14); (14,1); (-14,-1); (-1,-14); (2,7); (7,2); (-2,-7); (-7,-2)$

Đến đây thì đơn giản rồi.

c.

$x(y-2)=-19$, bạn làm tương tự

d. Tương tự

1: \(=6x^2+2x-15x-5-x^2+6x-9+4x^2+20x+25-27x^3-27x^2-9x-1\)

=-27x^3-18x^2+4x+10

2: =4x^2-1-6x^2-9x+4x+6-x^3+3x^2-3x+1+8x^3+36x^2+54x+27

=7x^3+37x^2+46x+33

5:

\(=25x^2-1-x^3-27-4x^2-16x-16-9x^2+24x-16+\left(2x-5\right)^3\)

\(=8x^3-60x^2+150-125+12x^2-x^3+8x-60\)

=7x^3-48x^2+8x-35