Thu gọn
A=53+54+55+.......+5100
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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:
\(\sqrt{x}+3\) | 5 |
\(x\) | 4 |
Vậy biểu thức nguyên khi x=4
643 x 48 x 164
= (26)3 \(\times\) (22)8 \(\times\) (24)4
= 218 \(\times\) 216 \(\times\) 216
= 250
2x+2-2x=96
=>2x\(\cdot\)22-2x=96
=>2x(22-1)=96
=>2x\(\cdot\)3=96
=>2x=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.`
\(...=\dfrac{152}{10}-\dfrac{15}{9}+\dfrac{48}{10}-\dfrac{4}{19}=\dfrac{76}{5}-\dfrac{5}{3}+\dfrac{24}{5}-\dfrac{4}{19}\)
\(=\dfrac{76}{5}-\dfrac{5}{3}+\dfrac{24}{5}-\dfrac{4}{19}=\dfrac{76}{5}+\dfrac{24}{5}-\dfrac{5}{3}-\dfrac{4}{19}\)
\(=\dfrac{100}{5}-\dfrac{5}{3}-\dfrac{4}{19}=20-\dfrac{5}{3}-\dfrac{4}{19}=\dfrac{20.57-5.19-4.3}{57}=\dfrac{1033}{57}\)
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.
\(A=5^3+5^4+5^5+...+5^{100}\)
\(A=5^3\left(1+5^1+5^2+...+5^{97}\right)\)
\(A=5^3.\dfrac{5^{97+1}-1}{5-1}=\dfrac{5^3}{4}.\left(5^{98}-1\right)\)
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