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(14,78-a)/(2,87+a)=4/1
14,78+2,87=17,65
Tổng số phần bằng nhau là 4+1=5
Mỗi phần có giá trị bằng 17,65/5=3,53
=>2,87+a=3,53
=>a=0,66.
a) A= 54 . 34- (152-1).(152+1)
=(5.3)4-154-1
=154-154-1
=-1
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\(a,=15\left(64+36\right)+100\cdot25+100\cdot60\\ =100\left(15+25+60\right)=100\cdot100=10000\\ b,Sửa:47^2+48^2-25^2+94\cdot48=\left(47+48\right)^2-25^2\\ =95^2-25^2=\left(95-25\right)\left(95+25\right)=70\cdot120=8400\)
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a) Ta có 15.64 + 25.100 + 36.15 + 60.100
= (15.64 + 36.15) + (25.100 + 60.100)
= 100.(15 + 85) = 10000.
b) Ta có 47 2 + 48 2 - 25 + 94.48
= ( 47 2 +2.47.48+ 48 2 ) - 5 2 = ( 47 + 48 ) 2 - 5 2 =9000.
c) Ta có 93 -92.(-l)-9.11 + (-l).ll
= (93 +92)-(9.11 + 1.11)
= 92(9 +1) -ll.(9 + l) = 700.
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1.
$=153^2+2.47.153+47^2=(153+47)^2=200^2=40000$
2.
$=1,24^2-2.1,24.0,24+0,24^2=(1,24-0,24)^2=1^2=1$
3. Không phù hợp để tính nhanh
4.
$=15^8-(15^8-1)=1$
5.
$=(1^2-2^2)+(3^2-4^2)+(5^2-6^2)+...+(2019^2-2020^2)$
$=(1-2)(1+2)+(3-4)(3+4)+(5-6)(5+6)+...+(2019-2020)(2019+2020)$
$=(-1)(1+2)+(-1)(3+4)+(-1)(5+6)+....+(-1)(2019+2020)$
$=(-1)(1+2+3+4+....+2019+2020)=(-1).2020(2020+1):2=-2041210$
6:
\(\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =1.\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^4-1\right)\left(2^4+1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^8-1\right)....\left(2^{2020}+1\right)+1\\ =\left(2^{2020}-1\right)\left(2^{2020}+1\right)+1\\ =2^{4040}-1+1=2^{4040}\)
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a) 2,83.5,68-2,83.4,68+1,17.5,68-1,17.4,68
= 2,83.(5,86-4,86)+1,17.(5,86-4,86)=2,83.1+1,17.1=4
b) 1112-1372-482+96.137
= 1112-(1372-2.48.137+482)=1112-(137-48)2=1112-892=(111-89)(111+89)=22.200=4400
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a) \(153^2-53^2=\left(153-53\right)\left(153+53\right)=100.206=20600\)
b)
\(\left(2020^2-2019^2\right)+\left(2018^2-2017^2\right)+...+\left(2^2-1^2\right)\\ =\left(2020+2019\right)\left(2020-2019\right)+\left(2018+2017\right)\left(2018-2017\right)+...+\left(2+1\right)\left(2-1\right)\\ =2020+2019+2018+2017+...+2+1\\ =\dfrac{\left(2020+1\right)2020}{2}=2041210\)
Lời giải:
a. $153^2-53^2=(153-53)(153+53)=100.206=20600$
b.
$2020^2-2019^2+2018^2-2017^2+...+2^2-1^2$
$=(2020^2-2019^2)+(2018^2-2017^2)+...+(2^2-1^2)$
$=(2020-2019)(2020+2019)+(2018-2017)(2018+2017)+...+(2-1)(2+1)$
$=2020+2019+2018+2017+...+2+1$
$=\frac{2020.2021}{2}=2041210$
![](https://rs.olm.vn/images/avt/0.png?1311)
\(100^2-99^2+98^2-97^2+...+2^2-1^2\)
\(=\left(100-99\right)\left(100+99\right)+\left(98-97\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\)
\(=199+195+...+3\)
Số lượng số hạng:
\(\left(199-3\right):4+1=50\) (số hạng)
Tổng:
\(\left(3+199\right)\times50:2=5050\)
Lời giải:
$=(100^2-99^2)+(98^2-97^2)+....+(2^2-1^2)$
$=(100-99)(100+99)+(98-97)(98+97)+...+(2-1)(2+1)$
$=100+99+98+97+...+2+1=100(100+1):2=5050$