c, 80% . X + 2/3 X = 286
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1. A) 225886 + 779 × 8
= 225886 + 6232
= 232118
B) 125 × 5 × 20 × 8
= (125 × 8) × (5 × 20)
= 1000 × 100
= 100000
C) 47286 : 2 + 14765
= 23643 + 14765
= 38408
D) 91428 - 23560 : 5
= 91428 - 4712
= 86716
3. A) 36 × 532 + 63 × 532 + 532
= 532 × (36 + 63 + 1)
= 532 × 100
= 53200
B) 679 × 123 + 679 - 679 × 24
= 679 × (123 + 1 - 24)
= 679 × 100
= 67900
C) 245 × 327 - 245 × 18 - 9 × 245
= 246 × (327 - 18 - 9)
= 245 × 300
= 73500
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3. Tính bằng cách thuận tiện nhất
A, 36 x 532 + 63 x 532 + 532
= (36 + 63 + 1) x 532 = 100 x 532 = 53 200
B, 679 x 123 + 679 - 679 x 24
= 679 x (123 + 1 - 24)
= 679 x 100 = 67 900
C, 245 x 327 - 245 x 18 - 9 x 245
= 245 x (327 - 18 - 9)
= 245 x 300
= 73 500
Bài 2:
a: \(6\cdot\left(x+9845\right)=29042\)
=>\(x+9845=\dfrac{29042}{6}=\dfrac{14521}{3}\)
=>\(x=\dfrac{14521}{3}-9845=-\dfrac{15014}{3}\)
b: \(\left(x:3\right)\cdot8=8\cdot3198\)
=>\(x:3=3198\)
=>\(x=3198\cdot3=9594\)
Bài 1:
a: \(225886+779\cdot8\)
\(=225886+6232\)
\(=232118\)
b: \(125\cdot5\cdot20\cdot8\)
\(=\left(125\cdot8\right)\cdot\left(5\cdot20\right)\)
\(=1000\cdot100=100000\)
c: \(47286:2+14765\)
\(=23643+14765\)
=38408
d: \(91428-23560:5\)
\(=91428-4712\)
=86716
![](https://rs.olm.vn/images/avt/0.png?1311)
2x - 12 = 18................................
2x = 30 ........................................
x = 15.....................................
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a, \(x+30\%x+1,5x=2,5\\ < =>x+0,3x+1,5x=2,5\\ < =>\left(1+0,3+1,5\right)x=2,5\\ < =>2,5x=2,5\\ =>x=\dfrac{2,5}{2,5}=1\)
b, \(2\left(3x-4\right)-3\left(x+2\right)=3\\ < =>6x-8-3x-6=3\\ < =>6x-3x=3+8+6\\ < =>3x=17\\ =>x=\dfrac{17}{3}\)
c, \(-110+7x-80=25+2x-80\\ < =>-110-80+80-25=2x-7x\\ < =>-135=-5x\\ =>x=\dfrac{-135}{-5}=27\)
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Xét khai triển:
\(\left(x+1\right)^n=C_n^0+C_n^1x+C_n^2x^n+C_n^3x^3+...+C_n^nx^n\)
Đạo hàm 2 vế:
\(n\left(x+1\right)^{n-1}=C_n^1+2C_n^2x+3C_n^3x^2+...+nC_n^nx^{n-1}\)
Thay \(x=1\) vào ta được:
\(n.2^{n-1}=C_n^1+2C_n^2+3C_n^3+...+nC_n^2=256n\)
\(\Rightarrow2^{n-1}=256=2^8\Rightarrow n=9\)
Câu 2:
\(\left(x-2\right)^{80}=a_0+a_1x+a_2x^2+a_3x^3+...+a_{80}x^{80}\)
Đạo hàm 2 vế:
\(80\left(x-2\right)^{79}=a_1+2a_2x+3a_3x^2+...+80a_{80}x^{79}\)
Thay \(x=1\) ta được:
\(80\left(1-2\right)^{79}=a_1+2a_2+3a_3+...+80a_{80}\)
\(\Rightarrow S=80.\left(-1\right)^{79}=-80\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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) \(7^{x+3}-7^{x+1}=16464\Leftrightarrow7^x\left(7^3-7\right)=16464\Leftrightarrow7^x=49\Leftrightarrow x=2\)
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a) 156 - 2 . x = 80
2 . x = 156 - 80
2 . x = 76
x= 76 : 2
x = 38
b) 315 + 5 . x = 200
5 . x = 200 - 315
5 . x = -115
x= -115 : 5
x = -23
c) 5 . ( x + 3 ) - 20 = 40
5 . ( x +3) = 40+20
5. ( x + 3) =60
x +3 =60:5
x + 3= 12
x = 12 - 3
x =9
80% x X + 2/3 x X = 286
4/5 x X + 2/3 x X =286
( 4/5 + 2/3) x X = 286
22/15 x X = 286
X = 286 : 22/15
X = 195
~ Hok Tốt ~
X.(80%+2/3)=286
X.(4/5+2/3)=286
X.(12/15+10/15)=286
X.22/15=286
X=286:22/15
X=195
Vậy X=195