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2 + 4 + 6 + 8 + ... + 2.x = 210
=> 2.1 + 2.2 + 2.3 +2.4 + ... + 2.x = 210
=> 2.( 1 + 2 + 3 + 4 + ... +x ) = 210
=> 2. [ x.( x+ 1) /2 ] = 210
=> x. ( x + 1 ) = 210
hay x.( x + 1) = 14.(14 + 1)
Vậy x = 14
2+4+6+8+...+2x=210
+) Ta có : 2.1+2.2+2.3+2.4+...+2x=210
=>2.(1+2+3+...x) =210
1+2+3+...+x= 210:2
1+2+3+...+x= 105
(x+1).x:2=105 =>(x+1).x=210 =>15.14=210 +) Vậy x=14
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Bài 2:
a: Ta có: \(2^{x+1}\cdot3^y=12^x\)
\(\Leftrightarrow2^{x+1}\cdot3^y=2^{2x}\cdot3^x\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+1=2x\\x=y\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=1\end{matrix}\right.\)
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2 + 4 + 6 +...+ 2x = 210
<=> 2 . ( 1 + 2 + 3 + ... + x ) = 210
<=> 2 . [ x . ( x + 1 ) / 2 ] = 210
<=> x . ( x + 1 ) = 210
<=> x = 14
2+4+6+...+2x=210
=>2(1+2+3+..+x)=210
=>(1+x)x/2(cong thuc tinh tong)=210/2
=>(1+x)x=210
=>(1+x)x=15.14
=>x=14
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`@` `\text {Ans}`
`\downarrow`
`2^x * 4 = 128`
`=> 2^x = 128 * 4`
`=> 2^x = 512`
`=> 2^x = 2^9`
`=> x = 9`
Vậy, `x = 9`
`x^15 = x`
`=> x^15 - x = 0`
`=> x(x^14 - 1) = 0`
`=>` TH1: `x = 0`
`TH2: x^14 - 1 = 0`
`=> x^14 = 1`
`=> x = 1`
Vậy, `x \in {0; 1}`
`(2x+1)^3 = 125`
`=> (2x+1)^3 = 5^3`
`=> 2x + 1 = 5`
`=> 2x = 5 - 1`
`=> 2x =4`
`=> x = 4 \div 2`
`=> x = 2`
Vậy,` x = 2.`
`(x - 5)^4 = (x-5)^6`
`=> (x-5)^4 - (x-5)^6 = 0`
`=> (x-5)^4 * [ 1 - (x-5)^2] = 0`
`=> - (x-6)(x-5)^4(x-4) = 0`
`TH1: (x - 5)^4 = 0`
`=> x - 5 = 0`
`=> x = 0 +5`
`=> x = 5`
`TH2: x - 6=0`
`=> x=6`
`TH3: x-4=0`
`=> x = 4`
Vậy, `x \in {4; 5; 6}`
a: =>2^x=32
=>x=5
b: =>x^15-x=0
=>x(x^14-1)=0
=>x=0; x=1;x=-1
c: =>2x+1=5
=>2x=4
=>x=2
d: =>(x-5)^4[(x-5)^2-1]=0
=>(x-5)(x-4)(x-6)=0
=>x=5;x=4;x=6
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Theo bài ra ta có : (y - 4)(1 + 2x) = 6 = 1 . 6 = 6. 1 = 2 . 3 = 3 .2
=> Ta có bảng giá trị :
y - 4 | 1 | 6 | 2 | 3 |
y | 5 | 10 | 6 | 7 |
1 + 2x | 6 | 1 | 3 | 2 |
x | 2,5 | 0 | 1 | 0,5 |
Vậy y = 10 thì x= 0 ; y = 6 thì x = 1
Ta có: 2+4+6+...+2.x=380
2.1+2.2+2.3+....+2.x=380
2.(1+2+3+...+x)=380
1+2+3+...+x= 380:2 = 190
(x+1) . ((x-1):1+1):2=190
(x+1). (x-1+1):2=190
(x+1).x= 190.2= 380
Vì 20.19=380 nên x=19
Vậy x=19
2 + 4 + 6 + ... + 2x = 380
2 . ( 1 + 2 + 3 + ... + x ) = 2 . 190
\(\Rightarrow\)1 + 2 + 3 + ... + x = 190
số số hạng vế trái là : ( x - 1 ) : 1 + 1 = x ( số )
tổng vế trái là : ( x + 1 ) . x : 2
hay ( x + 1 ) . x : 2 = 190
( x + 1 ) . x = 190 . 2
( x + 1 ) . x = 380
ta có : 380 = 19 . 20
suy ra x = 19