-108+2|x-11|=-80
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\(a,=-2\sqrt{5}+9\sqrt{5}-24\sqrt{5}-\sqrt{5}=-18\sqrt{5}\)
\(b,=2\sqrt{3}-5\sqrt{3}+4\sqrt{3}-7\sqrt{3}=-6\sqrt{3}\)
\(c,=3\sqrt{3}+7\sqrt{3}-9\sqrt{3}+11\sqrt{3}=12\sqrt{3}\)
a) Ta có: \(-\sqrt{20}+3\sqrt{45}-6\sqrt{80}-\dfrac{1}{5}\sqrt{125}\)
\(=-2\sqrt{5}+9\sqrt{5}-24\sqrt{5}-\dfrac{1}{5}\cdot5\sqrt{5}\)
\(=-17\sqrt{5}-\sqrt{5}=-18\sqrt{5}\)
b) Ta có: \(2\sqrt{3}-\sqrt{75}+2\sqrt{12}-\sqrt{147}\)
\(=2\sqrt{3}-5\sqrt{3}+4\sqrt{3}-7\sqrt{3}\)
\(=-6\sqrt{3}\)
Tính nhanh các tổng sau:
a) 2 + 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26 + 29
= ( 2+ 8 ) + ( 5 + 20) + ( 11 + 29 ) + ( 14 + 26 ) + ( 17 + 23 )
= 10 + 25 + 40 + 40 + 40
= 35 + 120
= 155
b) 120 + 116 + 112 + 108 + 104 + 100 + 96 + 92 + 88 + 84 + 80
= ( 120 + 80 ) + ( 116 + 84 )+ ( 112 + 88 ) + ( 108 + 92 ) + ( 104 + 96 ) + 100
= 200 + 200 + 200 + 200 + 200 + 100
= 200 x 5 + 100
= 1100
1) \(5^{x+1}-5^x=20\Leftrightarrow5^x\left(5-1\right)=20\Leftrightarrow5^x=5\Leftrightarrow x=1\)
2) \(2^x+2^{x+4}=544\Leftrightarrow2^x\left(1+2^4\right)=544\Leftrightarrow2^x=32\Leftrightarrow x=5\)
3) \(4^{2x+1}+4^{2x}=80\Leftrightarrow4^{2x}\left(4+1\right)=80\Leftrightarrow16^x=16\Leftrightarrow x=1\)
4) \(3^{2x+2}+3^{2x+1}=108\Leftrightarrow3^{2x}\left(3^2+3\right)=108\Leftrightarrow9^x=9\Leftrightarrow x=1\)
5) \(7^{x+3}-7^{x+1}=16464\Leftrightarrow7^x\left(7^3-7\right)=16464\Leftrightarrow7^x=49\Leftrightarrow x=2\)
\(-\dfrac{8}{11}.x=\dfrac{2}{5}.\dfrac{1}{4}\)
\(-\dfrac{8}{11}.x=\dfrac{2}{20}\)
\(-\dfrac{8}{11}.x=\dfrac{1}{10}\)
\(x=\dfrac{1}{10}:-\dfrac{8}{11}\)
\(x=-\dfrac{11}{81}\)
Chọn d
chuyển đổi lại : (7x - 3) : 12 = 13
=> (7x - 3) = 13 * 12
=> 7x - 3 = 156
=> 7x = 159
=> x= 159/7
[(7x - 31) : 5] * 36 = 7236
=> [(7x - 31) : 5] = 7236 : 36 = 201
=> (7x - 31) : 5 = 201
=> 7x - 31 = 1005
=> 7x = 1036
=> x = 148
1 + 2 + 3 + 4 + 5 +... + 100 + x = 5350
SSH : \(\left(100-1\right):1+1=100\)
=> tổng : \(\frac{\left(1+100\right)\cdot100}{2}=5050\)
=> 5050 + x = 5350
=> x = 5350 - 5050 = 300
80 - 9(x - 4) = 35
=> 9(x - 4) = 80 - 35 = 45
=> x - 4 = 45 : 9
=> x - 4 = 5
=> x = 9
(3x - 21) : 4 + 108 = 114
=> (3x - 21) : 4 = 114 - 108 = 6
=> 3x - 21 = 24
=> 3x = 45
=> x = 15
[(6x - 72) : 2 - 84]*14 = 2814
=> [(6x - 72) : 2 - 84] = 201
=> (6x - 72) : 2 - 84 = 201
=> (6x - 72) : 2 = 285
=> 6x - 72 = 570
=> 6x = 642
=> x = 107
28x + 12x = 80
=> 40x = 80
=> x = 2
249 - 7(1 + x) = 200
=> 7(1 + x) = 49
=> 1 + x = 7
=> x = 6
20 - [(x - 5) * 7 + 4] = 2
=> [(x - 5) * 7 + 4] = 18
=> (x - 5)*7 + 4 = 18
=> (x - 5) * 7 = 14
=> x - 5 = 2
=> x = 7
\(\frac{7x-33}{12}=13\)
\(7x-33=13\cdot12\)
\(7x-33=156\)
\(7x=156+33\)
\(7x=189\)
\(x=\frac{189}{7}=27\)
\(\frac{7x-31}{5}\cdot36=7236\)
\(\frac{7x-31}{5}=\frac{7236}{36}\)
\(\frac{7x-31}{5}=201\)
\(7x-31=201\cdot5\)
\(7x-31=1005\)
\(7x=1005+31\)
\(7x=1036\)
\(x=\frac{1036}{7}=148\)
\(1+2+3+4+5+..+100+x=5350\)
\(\left(1+2+3+4+5+...+100\right)+x=5350\)
Phần 1 + 2 + 3 + 4 + 5 + ... + 100 có số số hạng là :
\(\frac{100-1}{1}+1=100\) ( số hạng )
\(\Rightarrow\frac{\left(100+1\right)\cdot100}{2}+x=5350\)
\(5050+x=5350\)
\(x=5350-5050=300\)
\(80-9\left(x-4\right)=35\)
\(9\left(x-4\right)=80-35\)
\(9\left(x-4\right)=45\)
\(x-4=\frac{45}{9}\)
\(x-4=5\)
\(x=5+4=9\)
\(\frac{3x-21}{4}+108=114\)
\(\frac{3x-21}{4}=114-108\)
\(\frac{3x-21}{4}=6\)
\(3x-21=6\cdot4\)
\(3x-21=24\)
\(3x=24+21\)
\(3x=45\)
\(x=\frac{45}{3}=15\)
\(14\left(\frac{6x-72}{2}-84\right)=2814\)
\(3x-36-84=\frac{2814}{14}\)
\(3x-120=201\)
\(3x=201+120\)
\(3x=321\)
\(x=\frac{321}{3}=107\)
\(28x+12x=80\)
\(x\left(28+12\right)=80\)
\(x\cdot40=80\)
\(x=\frac{80}{40}=2\)
\(249-7\left(1+x\right)=200\)
\(-7\left(1+x\right)=200-249\)
\(-7\left(1+x\right)=-49\)
\(1+x=\frac{-49}{-7}\)
\(1+x=7\)
\(x=7-1=6\)
\(20-7\left(x-5\right)+4=2\)
\(20-7\left(x-5\right)=2-4\)
\(20-7\left(x-5\right)=-2\)
\(-7\left(x-5\right)=-2-20\)
\(-7\left(x-5\right)=-22\)
\(x-5=\frac{-22}{-7}\)
\(x=\frac{22}{7}+5=\frac{57}{7}\)
a)80-3.(x+4)=8
3.(x+4)=80-8=72
x+4=72:3=24
x+24-4=20
Vậy x=20
(x+1)+(x+3)+(x+5)+(x+7)+(x+9)+(x+11)=108
6x+36=108
6x=72
x=12
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(x+1)+(x+3)+(x+5)+(x+7)+(x+9)+(x+11)=108
( x + x + x + x + x + x ) + ( 1 + 3 + 5 + 7 + 9 + 11 ) = 108
6x + 36 = 108
6x = 108 - 36
6x = 72
x = 72 : 6
x = 12
\(-108+2\left|x-11\right|=-80\)
\(\Rightarrow2\left|x-11\right|=-80+108\)
\(\Rightarrow2\left|x-11\right|=28\)
\(\Rightarrow\left|x-11\right|=28:2\)
\(\Rightarrow\left|x-11\right|=14\)
\(\Rightarrow\orbr{\begin{cases}x-11=14\\x-11=-14\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=14+11\\x=-14+11\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=25\\x=-3\end{cases}}\)
Vậy \(x\in\left\{25;-3\right\}\)