\(999^4+999\)

\(=999\left(999^3+1\right)\)

\(=999\left(999+1\right)\left(999^2-999+1\right)\)

\(=999.1000.\left(999^2-999+1\right)\)có tận cùng là 3 chữ số 0

\(a,\frac{x^2+2.x.5+5^2+x^2-2.x.5+5^2}{x^2+25}\)

\(=\frac{2\left(x^2+25\right)}{x^2+25}=2\)

Vậy giá trị biểu thức không phụ thuộc vào x

\(b,\frac{4x^2+20x+25+25x^2-20x+4}{x^2+1}\)

\(=\frac{29\left(x^2+1\right)}{x^2+1}=29\)

Vậy gt biểu thức không phụ thuộc vào x

a)  \(\frac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}\)

   \(=\frac{x^2+10x+25+x^2-10x+25}{x^2+25}\)

   \(=\frac{2\left(x^2+25\right)}{x^2+25}=2\)

\(\Rightarrow\)đpcm

b)  \(\frac{\left(2x+5\right)^2+\left(5x-2\right)^2}{x^2+1}\)

\(=\frac{4x^2+20x+25+25x^2-20x+4}{x^2+1}\)

\(=\frac{29\left(x^2+1\right)}{x^2+1}=29\)

\(\Rightarrow\)đpcm

\(3x^{n-2}\left(x^{n+2}-y^{n+2}\right)+y^{n+2}\left(3x^{n-2}-y^{n-2}\right)\)

\(=3x^{2n}-3x^{n-2}y^{n+2}+y^{n+2}\left(3x^{n-2}-y^{n-2}\right)\)

\(=3x^{2n}-3x^{n-2}y^{n+2}+3x^{n-2}y^{n+2}-y^{2n}\)

\(=3x^{2n}-y^{2n}\)

\(3x^{n-2}\left(x^{n+2}-y^{n+2}\right)+y^{n+2}\left(3x^{n-2}-y^{n-2}\right)\)

\(=3x^{2n}-3x^{n-2}y^{n+2}+y^{n+2}\left(3x^{n-2}-y^{n-2}\right)\)

\(=3x^{2n}-3x^{n-2}y^{n+2}+3x^{n-2}y^{n+2}-y^{2n}\)

\(=3x^{2n}-y^{2n}\)

Cho mk xin cái li ke

\(A=x^2-x=x\left(x-1\right)\)

Với \(x\ge0\)

\(\Rightarrow A\ge0\)

Với\(x< 0\)

\(\Rightarrow x^2-x< 0\)

Vậy GTNN A là A < 0 <=> x < 0

Ta có : 

   B= x-x²

      = -(x-x²)

     = 1/4-(x²-x+1/4)

     = 1/4-(x-1/2)² < hoặc = 1/4

Vậy B_max= 1/4 <=> x=1/2

a)   \(x^3-2x^2-6x+12\)

\(=x^2\left(x-2\right)-6\left(x-2\right)\)

\(=\left(x-2\right)\left(x^2-6\right)\)

\(=\left(x-2\right)\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)

b)  \(x^4-7x^2+12\)

\(=x^4-3x^2-4x^2+12\)

\(=x^2\left(x^2-3\right)-4\left(x^2-3\right)\)

\(=\left(x^2-3\right)\left(x^2-4\right)\)

\(=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\left(x-2\right)\left(x+2\right)\)

c)  \(x^2-5x+4\)

\(=x^2-x-4x+4\)

\(=x\left(x-1\right)-4\left(x-1\right)\)

\(=\left(x-1\right)\left(x-4\right)\)

d)  \(3x^2+5x+2\)

\(=3x^2+3x+2x+2\)

\(=3x\left(x+1\right)+2\left(x+1\right)\)

\(=\left(x+1\right)\left(3x+2\right)\)

e)  \(x^3-x+3x^2y+3xy^2+y^3-y\)

\(=\left(x+y\right)^3-\left(x+y\right)\)

\(=\left(x+y\right)\left[\left(x+y\right)^2 -1\right]\)

\(=\left(x+y\right)\left(x^2+y^2+2xy-1\right)\)

a)x=5.9

b)4/9

a) 5/9

b)6/9