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