\(A=5^3+5^4+5^5+...+5^{100}\)

\(A=5^3\left(1+5^1+5^2+...+5^{97}\right)\)

\(A=5^3.\dfrac{5^{97+1}-1}{5-1}=\dfrac{5^3}{4}.\left(5^{98}-1\right)\)

5

x=1,y=1

Đẻ \(\dfrac{\sqrt[]{x}-2}{\sqrt[]{x}+3}\) là số nguyên khi

\(\left(\sqrt[]{x}-2\right)⋮\left(\sqrt[]{x}+3\right)\)

\(\Rightarrow\sqrt[]{x}-2-\left(\sqrt[]{x}+3\right)⋮\sqrt[]{x}+3\)

\(\Rightarrow\sqrt[]{x}-2-\sqrt[]{x}-3⋮\sqrt[]{x}+3\)

\(\Rightarrow-5⋮\sqrt[]{x}+3\)

\(\Rightarrow\left(\sqrt[]{x}+3\right)\in\left\{-1;1;-5;5\right\}\)

\(\Rightarrow x\in\left\{\varnothing;\varnothing;\varnothing;4\right\}\Rightarrow x\in\left\{4\right\}\left(x\in Z\right)\)

Ta có: \(\dfrac{\sqrt{x}-2}{\sqrt{x}+3}=\dfrac{\sqrt{x}+3-5}{\sqrt{x}+3}=1-\dfrac{5}{\sqrt{x}+3}\) nguyên khi:

5 ⋮ \(\sqrt{x}+3\)

\(\Rightarrow\sqrt{x}+3\inƯ\left(5\right)\)

Mà: \(Ư\left(5\right)=\left\{1;-1;5;-5\right\}\)

Và \(x\ge0\) nên \(\sqrt{x}+3\in\left\{5\right\}\)

Ta có bảng sau: 

Vậy biểu thức nguyên khi x=4

Đề yc gì em?

=262144x65536x65536

   64³ x 4⁸ x 16⁴

= (2⁶)³ \(\times\) (2²)⁸ \(\times\) (2⁴)⁴

= 2¹⁸ \(\times\) 2¹⁶ \(\times\) 2¹⁶

= 2⁵⁰

2^x+2-2^x=96

=>2^x\(\cdot\)2²-2^x=96

=>2^x(2²-1)=96

=>2^x\(\cdot\)3=96

=>2^x=96:3=32=2⁵

=>x=5

Vậy x=5

`@` `\text {Ans}`

`\downarrow`

\(2^{x+2}-2^x=96?\)

`\Rightarrow 2^x . 2^2 - 2^x = 96`

`\Rightarrow 2^x . (2^2 - 1) = 96`

`\Rightarrow 2^x . 3 = 96`

`\Rightarrow 2^x = 96 \div 3`

`\Rightarrow 2^x =32`

`\Rightarrow 2^x = 2^5`

`\Rightarrow x = 5`

Vậy, `x = 5.`

1033/57

\(...=\dfrac{152}{10}-\dfrac{15}{9}+\dfrac{48}{10}-\dfrac{4}{19}=\dfrac{76}{5}-\dfrac{5}{3}+\dfrac{24}{5}-\dfrac{4}{19}\)

\(=\dfrac{76}{5}-\dfrac{5}{3}+\dfrac{24}{5}-\dfrac{4}{19}=\dfrac{76}{5}+\dfrac{24}{5}-\dfrac{5}{3}-\dfrac{4}{19}\)

\(=\dfrac{100}{5}-\dfrac{5}{3}-\dfrac{4}{19}=20-\dfrac{5}{3}-\dfrac{4}{19}=\dfrac{20.57-5.19-4.3}{57}=\dfrac{1033}{57}\)

45-58+(-45)+(+58)-3=45-58-45+58-3=(45-45)+(58-58)-3=-3

(-57)-(-12)+3-(-57)=-57+12+3+57=(-57+57)+12+3=15

-(-24)-(-30)+(-24)-30+8=24+30-24-30+8=(24-24)+(30-30)+8=8

-(-12)+(+19)-(+12)+8-19=12+19-12+8-19=(12-12)+(19-19)+8=8

47-(-53)+(-47)-(+53)=47+53-47-53=(47-47)+(53-53)=0

-(+28)+32-(-28)+(-34)=-28+32+28-34=(-28+28)-(34-32)=-2

15-(+72)+(-15)+(+72)=15-72-15+72=(15-15)+(72-72)=0

20-(+46)+(-25)-(-46)=20-46-25+46=(20-25)+(46-46)=-5

28-(-32)+(-28)-32+5=28+32-28-32+5=(28-28)+(32-32)+5=5

-75+(-49)+(+75)+49-12=-75-49+75+49-12=(-75+75)+(49-49)-12=-12

\(...=45-58-45+58-3=-3\)

\(...=-57+12+3+57=15\)

\(...=24+30-24-30+8=8\)

\(...=12+19-12+8-19=8\)

\(...=47+53-47-53=0\)

\(...=-28+32+28-34=-2\)

\(...=15-72-15+72=0\)

\(...=20-46-25+46=-5\)

\(=...28+32-28-32+5=5\)

\(...=-75-49+75+49-12=-12\)

$(48-3.x):5=9$

$48-3.x=9.5$

$48-3.x=45$

$3.x=48-45$

$3.x=3$

$x=3:3$

$x=1$

( 48 - 3 .x ) : 5 = 9

⇒ 48 - 3 . x = 45

⇒ 3 . x = 3

⇒ x = 1

Vậy x = 1.

$11+2.(x-3)=15$

$2.(x-3)=15-11$

$2.(x-3)=4$

$x-3=4:2$

$x-3=2$

$x=2+3$

$x=5$

11 + 2. ( x - 3 ) = 15

⇒  2. ( x -3 ) = 26

⇒ x - 3 = 13

⇒ x = 16 

Vậy x = 16.