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a) x+(x+1)+(x+2)+(x+3)+...+(x+30)=1240
( x + x + x + x + ... + x ) + ( 1 + 2 + 3 +... + 30 ) = 1240
31x + 465 = 1240
31x = 1240 - 465
31x = 775
x = 775 : 31
x = 25
a) x+(x+1)+(x+2)+(x+3)+...+(x+30)=1240
( x + x + x + x + ... + x ) + ( 1 + 2 + 3 +... + 30 ) = 1240
31x + 465 = 1240
31x = 1240 - 465
31x = 775
x = 775 : 31
x = 25
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=>\(\frac{6\left(x-1\right)}{18}+\frac{9\left(3x-5\right)}{18}+\frac{2\left(2x\right)}{18}+\frac{2\left(-5x+3\right)}{18}=\frac{1}{2}\)
=>\(\frac{6x-6}{18}+\frac{27x-45}{18}+\frac{4x}{18}+\frac{-10x+6}{18}=\frac{1}{2}\)
=>\(\frac{\left(6x-6\right)+\left(27x-45\right)+4x+\left(-10x+6\right)}{18}=\frac{1}{2}\)
=>\(\frac{27x-45}{18}=\frac{1}{2}\)
=>54x-90=18
54x =108
=>x=2
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Bài 1:
Ta có: \(4-2\left(x+1\right)=2\)
\(\Leftrightarrow2\left(x+1\right)=2\)
\(\Leftrightarrow x+1=1\)
hay x=0
Bài 2:
Ta có: \(\left|2x-3\right|-1=2\)
\(\Leftrightarrow\left|2x-3\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=3\\2x-3=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=0\end{matrix}\right.\)
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1.
| x + 2 | = | 2 - 3x |
xét 2 trường hợp :
+) TH1 :
2 - 3x = x + 2
-3x + x = 2 + 2
2x = 4
x = 4 : 2 = 2
+) TH2 :
2 - 3x = - ( x + 2 )
2 - 3x = -x - 2
-3x - x = 2 - 2
-4x = 0
x = 0 : ( -4 )
x = 0
bài còn lại tương tự
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Vì 126⋮x;210⋮x⇒x∈ƯC(126;210)126⋮x;210⋮x⇒x∈ƯC(126;210)
Mà ƯCLN(126; 210) = 42
⇒x∈Ư(42)⇒x∈Ư(42)
Mặt khác, theo đề bài: 10 < x > 40
=> x ∈ tập rỗng
Vậy ko có gt x thỏa mãn
Vì: \(126⋮x,\) \(210⋮x\) \(\Rightarrow x\inƯC\left(126,210\right)\)
Ta có:
\(126=2.3^2.7\)
\(210=2.3.5.7\)
\(UCLN\left(126,210\right)=42\RightarrowƯC\left(42\right)=\left(1,2,3,6,7,14,21,42\right)\)
Mà 10<x<40 nên \(x\in\left(14,21\right)\)
Vậy \(x\in\left(14,21\right)\)
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\(a,2^{x+1}=32\\ 2^{x+1}=2^5\\ x+1=5\\ x=4\\ b,2^{2x}+2^{2x+1}=48\\ 2^{2x}+2\cdot2^{2x}=48\\ 3\cdot2^{2x}=48\\ 2^{2x}=16\\ 2^{2x}=2^4\\ 2x=4\\ x=2\)
\(c,3^x+5\cdot3^{x+1}=144\\ 3^x+15\cdot3^x=144\\ 16\cdot3^x=144\\ 3^x=9\\ 3^x=3^2\\ x=2\\ d,3^{x+5}=9^{x+1}\\ 3^{x+5}=3^{2x+2}\\ x+5=2x+2\\ x=3\)
-210 = (-1) + (-2) + (-3) + ... + (-x - 1) + (-x)
=> -210 = -(1 + 2 + 3 + ... + x + 1 + x)
=> 210 = 1 + 2 + 3 + ... + x + x + 1
=> 210 = \(\frac{\left(x+1+1\right).\left(x+1\right)}{2}\)
=> 420 = (x + 2) . (x + 1)
=> 21 . 20 = (x + 2) . (x + 1)
=> (19 + 2) . (19 + 1) = (x + 2) + (x + 1)
=> x = 19.
\(y=\frac{1}{x^2+\sqrt{x}}\)