1)  x⁴  - 2224x³ + 2223x² -2223x + 2223          tại x = 2002

thay x = 2002  vào biểu thức:

Ta có:  2002⁴  - 2224 * (2002)³ + 2223 * (2002)² - 2223 * 2002 + 2223 

= - 1 772 427 985 107

mình k biết

x² + xy + y² = 0

<=> x² = xy = y²

=> x = y = 0

đỡ hơn chưa??? mong các bn giúp mình vs

Vê trái: 

\(=\frac{2}{\left(x-1\right)\left(x+1\right)}+\frac{4}{\left(x-2\right)\left(x+2\right)}+...+\frac{20}{\left(x-10\right)\left(x+10\right)}\)

\(=\frac{\left(x+1\right)-\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{\left(x+2\right)-\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}+...+\frac{\left(x+10\right)-\left(x-10\right)}{\left(x+10\right)\left(x-10\right)}\)

\(=\frac{1}{x-1}-\frac{1}{x+1}+\frac{1}{x-2}-\frac{1}{x+2}+...+\frac{1}{x-10}-\frac{1}{x+10}\)

\(=\left(\frac{1}{x-1}+\frac{1}{x-2}+...+\frac{1}{x-10}\right)-\left(\frac{1}{x+1}+\frac{1}{x+2}+...+\frac{1}{x+10}\right)\)

Vế phải:

\(=\frac{\left(x+1\right)-\left(x-10\right)}{\left(x-10\right)\left(x+1\right)}+\frac{\left(x+2\right)-\left(x-9\right)}{\left(x-9\right)\left(x+2\right)}+...+\frac{\left(x+10\right)-\left(x-1\right)}{\left(x-1\right)\left(x+10\right)}\)

\(=\frac{1}{x-10}-\frac{1}{x+1}+\frac{1}{x-9}-\frac{1}{x+2}+...+\frac{1}{x-1}-\frac{1}{x+10}\)

\(=\left(\frac{1}{x-1}+\frac{1}{x-2}+...+\frac{1}{x-10}\right)-\left(\frac{1}{x+1}+\frac{1}{x+2}+...+\frac{1}{x+10}\right)\) = vế phải

=> đpcm

gọi chữ số tận cùng của 7ⁿ là:a

ta có:7ⁿ⁺⁴=7ⁿ.7⁴=(...a).2401=...a

=>đpcm

(a+b+c)²=(a+b)²+2(a+b)c+c²

          =a²+2ab+b²+2ac+2bc+c²

(a+b-c)²=(a+b)²-2(a+b)c+c²

           =a²+2ab+b²-2ab-2bc+c²

(a-b-c)²=(a-b)²-2(a-b)c+c²

        =a²-2ab+b²-2ac+2bc+c²

(2x+3y)²+2(2x+3y)+1=[(2x+3y)+1)]²=(2x+3y+1)²

9x²-6x+1=(3x)²-2.3x+1²=(3x-1)²