The greatest distinct 4-digits number : 9876

 The least 3-digit number is: 

The sum of 9876 and 100 is : 

 9876 + 100 = 9976

No isosceles triangles . Because 2 < 3 < 7 < 11

There is no equal edge 

We have : \(\dfrac{x^2-3x+2}{x^2+4x+5}=\dfrac{1}{2}\)

\(\Rightarrow\left(x^2-3x+2\right).2=x^2+4x+5\)

\(\Leftrightarrow2x^2-6x+4=x^2+4x+5\)

\(\Leftrightarrow2x^2-x^2-6x-4x=5-4\)

\(\Leftrightarrow x^2-10x-1=0\)

\(\Leftrightarrow x^2-10x+25-26=0\)

​ ​\(\Leftrightarrow\left(x-5\right)^2=26\)

=> x - 5 = ​ ​​\(\sqrt{26}\)

=> x = \(\sqrt{26}+5\)

We have : x - x² + x³ - x⁴

= (x - x²) + (x³ - x⁴)

= x(1 - x) + x³(1 - x)

= (1 - x)(x + x³)

= (1 - x).x(1 + x²)

b) ?

We have : x(x + 3) - x - 3 = 0

=> x(x + 3) - (x + 3) = 0

=> (x - 1)(x + 3) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)

2x - x + 3x - 2x = 0

=> -x + 3x = 0

=> 2x = 0

=> x = 0

1,x(x − 3) + x − 3 = 0

=> (x - 3)(x + 1) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\)

​\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)

We have : 516 - [340 + (-4 - 1)] 

= 516 - (340 - 5)

= 516 - 335 

= 181

We have : 2³ . x² = 32

=> 8.x² = 32

=> x² = 4

=> x = -2;2

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

20 + 20 = 40

Ta có : 100 x 5 = 500

Ta có : 100 + 100 = 200

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

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

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 4-digit number containing two digits, or three or both, is 9000 - 3584 = 5416 (number).

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 4-digit number containing two digits, or three or both, is 9000 - 3584 = 5416 (number).

Calling the two-digit 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

Calling the two-digit 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

The legs of 4 horses: 

he legs of  11 people: 

The total legs: