88 : 4 = ?
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Hướng dẫn giải:
a) 513 x 4 + 513 x 6
= 513 x (4 + 6)
= 513 x 10 = 5130
b) 88 x 9 – 88 x 8
= 88 x (9 – 8)
= 88 x 1 = 88
a) 513 x 4 + 513 x 6 = 513 x (4 + 6)
= 513 x 10
= 5 130
b) 88 x 9 - 88 x 8 = 88 x (9 - 8)
= 88 x 1
=88
![](https://rs.olm.vn/images/avt/0.png?1311)
\(288-\left(88+5^4\right)-\left(4x^4-200\right)=416\)
\(\Leftrightarrow288-88-625-4x^4+200=416\)
\(\Leftrightarrow-4x^4-225=416\)
\(\Leftrightarrow-4x^4=641\)(vô lý)
![](https://rs.olm.vn/images/avt/0.png?1311)
4/2.5+4/5.8+4/8.11+..........+4/17.20
=4/3.(3/2.5+3/5.8+3/8.11+...........3/17.20)
=4/3.(1/2-1/5+1/5-1/8+1/8-1/11+...................+1/17-1/20)
=4/3.(1/2-1/20)
=4/3.9/20
=3/5
![](https://rs.olm.vn/images/avt/0.png?1311)
\(288-\left(88+5^4\right)-\left(4x^4-200\right)=416\)
\(\Leftrightarrow288-88-625-4x^4+200=416\)
\(\Leftrightarrow-4x^4-225=416\)
\(\Leftrightarrow-4x^4=641\)(vô lý)
288 - (88 + 54) - (4x4 - 200) = 416
<=> 288 - 88 - 625 - 4x4 + 200 = 416
<=> 288 - 88 - 625 - 416 + 200 = 4x4
<=> -641 = 4x4
<=> x4 = -160,25
<=> x = \(-\sqrt[4]{160,25}\) = -3,557947288 \(\approx\) -3,56
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(A=1.3+2.4+3.5+4.6+...+99.101+100.102\)
\(A=1.\left(1+2\right)+2.\left(2+2\right)+3.\left(3+2\right)+4.\left(4+2\right)+....+99.\left(99+2\right)+100.\left(100+2\right)\)
\(A=\left(1^2+2^2+3^2+4^2+...+99^2+100^2\right)+\left(2+4+6+8+...+198+200\right)\)Đặt \(B=1^2+2^2+3^2+4^2+5^2+...+99^2+100^2\)
\(\Rightarrow B=\left(1^2+2^2+3^2+4^2+5^2+...+99^2+100^2\right)-2^2.\left(1^2+2^2+3^2+4^2+5^2+....+49^2+50^2\right)\)Tính dãy tổng quát \(C=1^2+2^2+3^2+4^2+5^2+...+n^2\)
\(C=1\left(0+1\right)+2\left(1+1\right)+3.\left(2+1\right)+4.\left(3+1\right)+5\left(4+1\right)+...+n\left[\left(n-1\right)+1\right]\)
\(C=\left[1.2+2.3+3.4+4.5+...+\left(n-1\right).n\right]+\left(1+2+3+4+5+....+n\right)\)
\(C=n.\left(n+1\right).\left[\left(n-1\right):3+1:2\right]=n.\left(n+1\right).\left(2n+1\right):6\)
Áp dụng vào B ta được:
\(B=100.101.201:6-4.50.51.101:6=166650\)
\(\Rightarrow A=166650+\left(200+2\right).100:2\)
\(\Rightarrow A=166650+10100=176750\)
Vậy A = 176750
Chúc bạn học tốt!!
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
21 : (y+3)x4=100-88
21:(y+3)x4=12
21:(y+3)=12 :4
21:(y+3)=3
y+3=21:3
y+3=7
y=7-3
y=4
Đáp số y=4
\(21:\left(y+3\right)\times4+88=100\)
\(21:\left(y+3\right)\times4=100-88\)
\(21:\left(y+3\right)\times4=12\)
\(21:\left(y+3\right)=12:4\)
\(21:\left(y+3\right)=3\)
\(y+3=21:3\)
\(y+3=7\)
\(y=7-3\)
\(y=4\)
88 : 4 = 22
88:4=22