Bài 1: 

Ta có: 

\(A=9x^4-15x^3-6x^2+5=3x^2\left(3x^2-5x\right)-6x^2+5=3x^2.2-6x^2+5=6x^2-6x^2+5=5\)

Vậy,  \(A=5\)

Bài 2: Ta có:

\(3^{15}+3^{16}+3^{17}=3^{15}+3^{15}.3+3^{15}.3^2=3^{15}.\left(1+3+3^2\right)=3^{15}.13\)

\(\Rightarrow3^{15}.13\)  chia hết cho  \(13\)

Do đó:  \(3^{15}+3^{16}+3^{17}\)  chia hết cho  \(13\)

\(\dfrac{3}{5}+\dfrac{4}{7}+\dfrac{2}{5}+\dfrac{1}{7}+\dfrac{2}{7}\\ =\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+\left(\dfrac{4}{7}+\dfrac{1}{7}+\dfrac{2}{7}\right)\\ =\dfrac{5}{5}+\dfrac{7}{7}\\ =1+1\\ =2\)

   3/5 + 4/7 + 2/5 + 1/7 + 2/7

=(3/5 + 2/5) + (4/7 + 1/7 + 2/7)

= 1 + 1 = 2

3/5 và 2/5 có mẫu chung là 5, 2+3 = 5 => 5/5 = 1

4/7, 1/7 và 2/7 có mẫu chung là 7, 4+1+2 = 7 => 7/7 = 1

\(1,\\ a,=6x^4y^4-x^3y^3+\dfrac{1}{2}x^4y^2\\ b,=4x^3+5x^2-8x^2-10x+12x+15\\ =4x^3-3x^2+2x+15\\ 2,\\ a,=7\left(x^2-6x+9\right)=7\left(x-3\right)^2\\ b,=\left(x-y\right)^2-36=\left(x-y-6\right)\left(x-y+6\right)\\ 3,\\ \Leftrightarrow x\left(x^2-0,36\right)=0\\ \Leftrightarrow x\left(x-0,6\right)\left(x+0,6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=0,6\\x=-0,6\end{matrix}\right.\)

\(a,\dfrac{4}{5}\times\dfrac{7}{3}\times\dfrac{3}{4}=\dfrac{4\times7\times3}{5\times3\times4}=\dfrac{7}{5}\)

\(b,\left(\dfrac{1}{2}+\dfrac{1}{3}\right)\times\dfrac{1}{4}\)

\(=\left(\dfrac{3}{6}+\dfrac{2}{6}\right)\times\dfrac{1}{4}\)

\(=\dfrac{5}{6}\times\dfrac{1}{4}\)

\(=\dfrac{5}{24}\)

\(c,\left(\dfrac{2}{3}+\dfrac{2}{5}\right)\times\dfrac{2}{7}\)

\(=\left(\dfrac{10}{35}+\dfrac{6}{35}\right)\times\dfrac{2}{7}\)

\(=\dfrac{16}{15}\times\dfrac{2}{7}\)

\(=\dfrac{32}{105}\)

Cách `1`

`a)4/5 xx 7/3 xx 3/4`

`=28/15 xx 3/4`

`=84/60`

`=7/5`

__

`b)(1/2+1/3)xx1/4`

`=(3/6+2/6)xx1/4`

`=5/6xx1/4`

`=5/24`

__

`c)(2/3+2/5)xx2/7`

`=(10/15+6/15)xx2/7`

`=16/15xx2/7`

`=32/105`

___________________________

Cách `2`:

`a)4/5 xx 7/3 xx 3/4`

`=4/5 xx (7/3 xx 3/4)`

`=4/5 xx 7/4`

`=7/5`

__

`b)(1/2+1/3)xx1/4`

`=1/2 xx 1/4 + 1/3 xx 1/4`

`= 1/8 + 1/12`

`= 3/24+2/24`

`=5/24`

__

`c)(2/3+2/5)xx2/7`

`=2/3 xx 2/7 + 2/5 xx 2/7`

`=4/21 + 4/35`

`= 20/105+12/105`

`=32/105`

`#QiN`

So phan 8 trang chiem la 

     1-(\(\frac{1}{2}\)+\(\frac{1}{4}\))=\(\frac{1}{4}\)

So trang co la

   8:\(\frac{1}{4}\)=32(trang)

`(4\sqrt{6}+x)^2=8^2+(6+\sqrt{x^2+4})^2`

`<=>96+8\sqrt{6}x+x^2=64+36+12\sqrt{x^2+4}+x^2+4`

`<=>2\sqrt{6}x-2=3\sqrt{x^2+4}`    `ĐK: x >= \sqrt{6}/6`

`<=>24x^2-8\sqrt{6}x+4=9x^2+36`

`<=>15x^2-8\sqrt{6}x-32=0`

`<=>x^2-[8\sqrt{6}]/15x-32/15=0`

`<=>(x-[4\sqrt{6}]/15)^2-64/25=0`

`<=>|x-[4\sqrt{6}]/15|=8/5`

`<=>[(x=[24+4\sqrt{6}]/15 (t//m)),(x=[-24+4\sqrt{6}]/15(ko t//m)):}`

Ta có: \(\frac{x+2}{y+10}\)\(=\)\(\frac{1}{5}\)\(\Rightarrow\)\(5\left(x+2\right)=y+10\)(1)

             \(y-3x=2\)\(\Rightarrow\)\(y+2=3x\)                              (2)

Thay (2) vào (1) ta có:

\(5\left(x+2\right)=\left(y+2\right)+8\)

\(5x+10=3x+8\)

\(5x-3x=8-10\)

\(2x=-2\)

\(x=-2:2\)

\(x=-1\)

Vậy: x=-1

Chúc bạn làm bài tốt!

A=|x - 2009| + |x - 2010| + |x - 2011| 

*TH1: Xét x ≤ 2009 ; khi đó 

. A = 2009 - x + 2010 - x + 2011 -x 

. A = 6030 - 3x 

có x ≤ 2009 --> -x ≥ -2009 --> -3x ≥ -6027 --> 6030 - 3x ≥ 3 

Dấu " = " <=> x = 2009 

--> Amin = 3 <=> x = 2009 

*TH2 : Xét 2009 < x ≤ 2010 ; ta có 

. A = x - 2009 + 2010 - x + 2011 - x 

. A = 2012 - x 

có x ≤ 2010 --> -x ≥ -2010 --> 2012 - x ≥ 2 

--> Amin = 2 <=> x = 2010 

*TH3 : Xét 2010 < x < 2011 ; ta có : 

. A = x - 2009 + x - 2010 + 2011 - x 

. A = x - 8 > 2010 - 8 = 2002 --> không có min 

*TH4 : Xét x ≥ 2011 ; ta có : 

. A = x - 2009 + x - 2010 + x - 2011 

. A = 3x - 6030 ≥ 3.1011 - 6030 = 3 

Dấu " = " <=> xảy ra <=> x = 2011 

--> Amin = 3 <=> x = 2011 

** Kết hợp các trường hợp trên lại ta có : 

Amin = 2 <=> x = 2010 

oái,sai rồi

`Answer:`

\(\frac{2-x}{2009}-1=\frac{1-x}{2010}-\frac{x}{2011}\)

\(\Leftrightarrow\frac{2-x}{2009}+1=\frac{1-x}{2010}+1-\frac{x}{2011}+1\)

\(\Leftrightarrow\frac{2011-2}{2009}=\frac{2011-x}{2010}-\frac{x-2011}{2011}\)

\(\Leftrightarrow\left(2011-x\right)\left(\frac{1}{2009}-\frac{1}{2010}-\frac{1}{2011}\right)=0\)

Mà \(\frac{1}{2010}+\frac{1}{2011}\ne\frac{1}{2009}\)

\(\Rightarrow2011-x=0\Leftrightarrow x=2011\)

3, 2x(x^2-8x+16)-(x+5)(x^2-4)+2(x^2+10x+25)-x+1

=2x^3-16x^2+32x-(x^3-4x+5x^2-20)+2x^2+20x+50-x+1

=2x^3-16x^2+32x-x^3+4x-5x^2+20+2x^2+20x+50-x+1

=x^3-19x^2+55x+71