123x23 56x32 89x20 3456x89
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Dũng cho Bình số viên bi là:
\(56x\dfrac{1}{4}=14\) ( viên )
Dũng cho Bảo số viên bi là:
\(56x\dfrac{3}{7}=24\) ( viên )
Vậy Dũng còn số viên bi là:
\(56-14-24=18\) ( viên )
Đ/S:...
![](https://rs.olm.vn/images/avt/0.png?1311)
20% của 15 là:
\(15.20:100=3\)
Vậy \(20\%\) của \(15\) là: \(3\)
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A = (2 + 2²) + (2³ + 2⁴) + ... + (2⁵⁹ + 2⁶⁰)
= 6 + 2².(2 + 2²) + ... + 2⁵⁸.(2 + 2²)
= 6 + 2².6 + ... + 2⁵⁸.6
= 6.(1 + 2² + ... + 2⁵⁸) ⋮ 6
A = (2 + 2² + 2³) + (2⁴ + 2⁵ + 2⁶) + ... + (2⁵⁸ + 2⁵⁹ + 2⁶⁰)
= 2(1 + 2 + 2²) + 2⁴.(1 + 2 + 2²) + ... + 2⁵⁸.(1 + 2 + 2²)
= 2.7 + 2⁴.7 + ... + 2⁵⁸.7
= 7.(2 + 2⁴ + ... + 2⁵⁸) ⋮ 7
Vậy A ⋮ 6 và A ⋮ 7
\(A\) chia hết cho \(7\):
\(A=2+2^2+2^3+...+2^{60}\)
\(A=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{58}+2^{59}+2^{60}\right)\)
\(A=2.\left(1+2+2^2\right)+2^4.\left(1+2+2^2\right)+...+2^{58}+\left(1+2+2^4\right)\)
\(A=\left(1+2+2^2\right).\left(2+2^4+2^7+...+2^{58}\right)\)
\(A=7.\left(2+2^4+2^7+...+2^{58}\right)⋮7\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{8^2.125.9^2-32.5^3.81}{20^3.3^4-6^8.5^4}\)
\(=\dfrac{2^6.5^3.3^4-2^5.5^3.3^4}{4^3.5^3.3^4-2^8.3^8.5^4}\)
\(=\dfrac{2^6.5^3.3^4-2^5.5^3.3^4}{2^6.5^3.3^4-2^8.3^8.5^4}\)
\(=\dfrac{2^5.5^3.3^4\left(2-1\right)}{2^6.5^3.3^4\left(1-2^2.3^4.5\right)}\)
\(=\dfrac{2^5.5^3.3^4.1}{2^6.5^3.3^4\left(1-810\right)}\)
\(=\dfrac{1}{2.\left(-809\right)}\)
\(=-\dfrac{1}{1618}\)
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\(=\left(x^3-x^2\right)-\left(x-1\right)\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x^2-1\right)\left(x-1\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x-1\right)\)
\(=\left(x-1\right)^2\left(x+1\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: \(2003^{2003}+1=2003^{2002+1}+1và2003^{2004}+1=2003^{2003+1}+1\)
\(\Rightarrow A>B\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x² - 4x - y² + 4
= (x² - 4x + 4) - y²
= (x - 2)² - y²
= (x - y - 2)(x + y - 2)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{2x+1}{18}=\dfrac{5}{2}\)
\(\Rightarrow2\left(2x+1\right)=5\cdot18\)
\(\Rightarrow4x+2=90\)
\(\Rightarrow4x=90-2=88\)
\(\Rightarrow x=\dfrac{88}{4}=22\)
123 x 23 = 2829
56 x 32 = 1792
89 x 20 = 1780
3456 x 89 = 307584