5x+(1+2+3+4+5)=65

5x+15=65

5x=50

x=10

5x+1+2+3+4+5=65

=>5x+15=65

=>5x=50

=>x=10

\(5x+\frac{5.6}{2}=65\Rightarrow x=\frac{65-15}{5}=10\)

1: =>5(2x+6)=40

=>2x+6=8

=>2x=2

=>x=1

2: =>12-(x+3)=256:64=4

=>(x+3)=8

=>x=5

3: =>2x-1=3 hoặc 2x-1=-3

=>x=2 hoặc x=-1

4: \(\Leftrightarrow3^{x+2017}=3^{2015}\)

=>x+2017=2015

=>x=-2

1: =>5(2x+6)=40

=>2x+6=8

=>2x=2

=>x=1

2: =>12-(x+3)=256:64=4

=>(x+3)=8

=>x=5

3: =>2x-1=3 hoặc 2x-1=-3

=>x=2 hoặc x=-1

4: \Leftrightarrow3^{x+2017}=3^{2015}⇔3x+2017=32015

=>x+2017=2015

=>x=-2

a.

Đặt \(\left\{{}\begin{matrix}\sqrt[3]{x+2}=a\\\sqrt[3]{x-2}=b\end{matrix}\right.\) ta được:

\(2a^2-b^2=ab\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}a^3=b^3\\8a^3=-b^3\end{matrix}\right.\)

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

\(\Leftrightarrow x=-\dfrac{14}{9}\)

b.

Đặt \(\left\{{}\begin{matrix}\sqrt[3]{65+x}=a\\\sqrt[3]{65-x}=b\end{matrix}\right.\)

\(\Rightarrow a^2+4b^2=5ab\)

\(\Leftrightarrow\left(a-b\right)\left(a-4b\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}a=b\\a=4b\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a^3=b^3\\a^3=64b^3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}65+x=65-x\\65+x=64\left(65-x\right)\end{matrix}\right.\)

\(\Leftrightarrow...\)

c.

Đặt \(\left\{{}\begin{matrix}\sqrt[3]{x+2}=a\\\sqrt[3]{x+1}=b\end{matrix}\right.\)

\(\Rightarrow a+b=1+ab\)

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

\(\Leftrightarrow\left[{}\begin{matrix}a=1\\b=1\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a^3=1\\b^3=1\end{matrix}\right.\)

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

\(\Leftrightarrow...\)

b, ĐKXĐ: \(x\ge\frac{5}{2}\)

\(pt\Leftrightarrow\sqrt{2x+4-6\sqrt{2x-5}}+\sqrt{2x-4+2\sqrt{2x-5}}=4\)

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

\(\Leftrightarrow\sqrt{2x-5}=3\)

\(\Leftrightarrow x=7\left(tm\right)\)

a, ĐKXĐ: \(x\ge5\)

\(pt\Leftrightarrow\sqrt{x-5+4\sqrt{x-5}+4}+\sqrt{x-5+8\sqrt{x-5}+16}=0\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x-5}+2\right)^2}+\sqrt{\left(\sqrt{x-5}+4\right)^2}=0\)

\(\Leftrightarrow2\sqrt{x-5}+6=0\)

\(\Leftrightarrow\sqrt{x-5}=-3\)

Phương trình vô nghiệm

`a,`\(2^x -15= 2^4+1\)

`-> 2^x-15=17`

`-> 2^x=17+15`

`-> 2^x=32`

`-> 2^x=2^5`

`-> x=5`

`b,` Có phải đề là \(\dfrac{x+1}{65}+\dfrac{x+2}{64}=\dfrac{x+3}{63}+\dfrac{x+4}{62}\) ?

`=>`\(\dfrac{x+1}{65}+1+\dfrac{x+2}{64}+1=\dfrac{x+3}{63}+1+\dfrac{x+4}{62}+1\)

`=>`\(\dfrac{x+1+65}{65}+\dfrac{x+2+64}{64}-\dfrac{x+3+63}{63}-\dfrac{x+4+62}{62}=0\)

`=>`\(\dfrac{x+66}{65}+\dfrac{x+66}{64}-\dfrac{x+66}{63}-\dfrac{x+66}{62}=0\)

`=>`\(\left(x+66\right)\left(\dfrac{1}{65}+\dfrac{1}{64}-\dfrac{1}{63}-\dfrac{1}{62}\right)=0\)

Mà `1/65+1/64-1/63-1/62 \ne 0`

`-> x+66=0`

`-> x=-66`

a: =>2^x=2^4+16=32

=>x=5

b: Sửa đề: \(\dfrac{x+1}{65}+\dfrac{x+2}{64}=\dfrac{x+3}{63}+\dfrac{x+4}{62}\)

=>\(\left(\dfrac{x+1}{65}+1\right)+\left(\dfrac{x+2}{64}+1\right)=\left(\dfrac{x+3}{63}+1\right)+\left(\dfrac{x+4}{62}+1\right)\)

=>x+66=0

=>x=-66

a) 26                  b) 13
c) 36;48;60      d) 5

a) 2.(x+4)+5=65

2.(x+4)=65-5

2.(x+4)=60

x+4=60:2

x+4=30

x=30-4=26

b)(x-5)2=16

x+5=16:2

x+5=8

x=8-5=3

1, 4\(^{x+1}\) + 4\(^0\) = 65

\(\Rightarrow\)4\(^{x+1}\) = 65 - 1

\(\Rightarrow\)x + 1      = 64 : 4

\(\Rightarrow\)x + 1      =  16

\(\Rightarrow\)x = 15

2) 10 + 2x = 16\(^{^2}\): 4\(^3\)

\(\Rightarrow\)10 + 2x = 4

\(\Rightarrow\)2x = 4 - 10

\(\Rightarrow\)2x = -6

\(\Rightarrow\)x = -3

Bài 1

a) 4^x+1 + 4⁰ = 65

=> 4^x+1 + 1 = 65

=> 4^x+1 = 64

=> 4^x+1 = 4³

=>x + 1 = 3

=> x = 2

b) 10 + 2x = 16²: 4³

=> 10 + 2x = ( 4² )² : 4³

=> 10 + 2x = 4⁴ : 4³

=> 10 + 2x = 4

=> 2x = -6

=> x = -3

c) 65 - 4^x+2 = 2018⁰

=> 65 - 4^x+2 = 1

=> 4^x+2 = 64

=> 4^x+2 = 4³

=> x + 2 = 3

=> x = 1

d) 2 < |x| < 4

=> x thuộc { -3 ; -4 }