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The greatest distinct 4digits number : 9876
The least 3digit number is: 100
The sum of 9876 and 100 is :
9876 + 100 = 9976

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No isosceles triangles . Because 2 < 3 < 7 < 11
There is no equal edge

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We have : \(\dfrac{x^23x+2}{x^2+4x+5}=\dfrac{1}{2}\)
\(\Rightarrow\left(x^23x+2\right).2=x^2+4x+5\)
\(\Leftrightarrow2x^26x+4=x^2+4x+5\)
\(\Leftrightarrow2x^2x^26x4x=54\)
\(\Leftrightarrow x^210x1=0\)
\(\Leftrightarrow x^210x+2526=0\)
\(\Leftrightarrow\left(x5\right)^2=26\)
=> x  5 = \(\sqrt{26}\)
=> x = \(\sqrt{26}+5\)

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We have : x  x^{2} + x^{3}  x^{4}
= (x  x^{2}) + (x^{3}  x^{4})
= x(1  x) + x^{3}(1  x)
= (1  x)(x + x^{3})
= (1  x).x(1 + x^{2})
b) ?

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The number of 4  digit numbers is:
(9999  1000): 1 + 1 = 9000 (number)
If you do not use numbers 2 and 3, then you have eight digits left to form units, tens and hundreds. Since zeros can not be used to make thousands of digits, there are only seven digits left to make thousands.According to the kernel rule, we have:
8 x 8 x 8 x 7 = 3584 (number)
Inference: A 4digit number containing two digits, or three or both, is 9000  3584 = 5416 (number).Answer : 5416 (number). 
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We have : x(x + 3)  x  3 = 0
=> x(x + 3)  (x + 3) = 0
=> (x  1)(x + 3) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x1=0\\x+3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
2x  x + 3x  2x = 0
=> x + 3x = 0
=> 2x = 0
=> x = 0

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1,x(x − 3) + x − 3 = 0
=> (x  3)(x + 1) = 0
\(\Leftrightarrow\left[{}\begin{matrix}x3=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=1\end{matrix}\right.\)

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We have : 516  [340 + (4  1)]
= 516  (340  5)
= 516  335
= 181

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We have : 2^{3} . x^{2} = 32
=> 8.x^{2} = 32
=> x^{2} = 4
=> x = 2;2

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Đặt A = 1.2.3 + 2.3.4 + 3.4.5 + ..... + 98.99.100
=> 4A = 1.2.3.4  1.2.3.4 + 2.3.4.5  2.3.4.5 + ..... + 98.99.100.101
=> 4A = 98.99.100.101
=> A = 98.99.100.101/4
=> A = 24497550

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20 + 20 = 40

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Ta có : 100 x 5 = 500

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Ta có : 100 + 100 = 200

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Total height of 2 boys are: 131.6 x 2 = 263.2(cm)
Total height of 4 girls are: 128.3 x 4 = 513.2(cm)
Total height of all children are: 263.2 + 513.2 = 776.4(cm)
The average height of all children are: 776.4 : 6 = 129.4(cm)Answer: 129.4cm

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Total height of 2 boys are: 131.6 x 2 = 263.2(cm)
Total height of 4 girls are: 128.3 x 4 = 513.2(cm)
Total height of all children are: 263.2 + 513.2 = 776.4(cm)
The average height of all children are: 776.4 : 6 = 129.4(cm)Answer: 129.4cm

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The number of 4digit numbers is: (9999  1000): 1 + 1 = 9000 (number)
If you do not use numbers 2 and 3, then you have eight digits left to form units, tens and hundreds. Since zeros can not be used to make thousands of digits, there are only seven digits left to make thousands. According to the kernel rule, we have: 8 x 8 x 8 x 7 = 3584 (number)
Inference: A 4digit number containing two digits, or three or both, is 9000  3584 = 5416 (number). 
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The number of 4digit numbers is: (9999  1000): 1 + 1 = 9000 (number)
If you do not use numbers 2 and 3, then you have eight digits left to form units, tens and hundreds. Since zeros can not be used to make thousands of digits, there are only seven digits left to make thousands. According to the kernel rule, we have: 8 x 8 x 8 x 7 = 3584 (number)
Inference: A 4digit number containing two digits, or three or both, is 9000  3584 = 5416 (number). 
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Calling the twodigit number written by Anna was: ab then the number Ben wrote was abab
The structural analysis of the number we are:
Abab = 100 x ab + ab = 101 x ab
The result of the division is: abab: ab = 101 x ab: ab = 101 
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Calling the twodigit number written by Anna was: ab then the number Ben wrote was abab
The structural analysis of the number we are:
Abab = 100 x ab + ab = 101 x ab
The result of the division is: abab: ab = 101 x ab: ab = 101 
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The legs of 4 horses: 4.4 = 16(legs)
The legs of 11 people: 11⋅2=22(legs)
The total legs: 16 + 22 = 38 (legs)