sai de

dau

Xet x≤2010 thi: -(x-2010)-(x-2011)=2012

=> -x+2010-x+2010-2012=0

=> -2x+2008=0

=> x=1004(TM)

Xet 2010≤x<2011 thi : (x-2010)-(x-2011)=2012

=> x-2010-x+2011-2012=0

=> 0x=2013

=> pt vo nghiem

Xet x>2011 thi: x-2010+x-2011=2012

=> 2x-4021-2012=0

=> 2x-6033=0

=> x=6033/2(TM)

a) (x²-y²)+(2x+2y)

= (x-y)(x+y)+2(x+y)

= (x+y)(x-y+2)

b) (3a²-6ab+3b²)-12c²

= 3(a²-2ab+b²)-12c²

= 3(a-b)²-3.(2c)²

= 3[(a-b)²-(2c)²]

= 3(a-b-2c)(a-b+2c)

c) (x²+2xy+y²)-25

= (x+y)²-25=(x+y-5)(x+y+5)

d) 81x²-(z²+6yz+9y²)=(9x)²-(z+3y)²=(9x-z-3y)(9x+z+3y)

A=x²-2.\(\dfrac{3}{2}x+\dfrac{9}{4}+\dfrac{11}{4}\)

=\(\left(x-\dfrac{3}{2}\right)^2+\dfrac{11}{4}\ge\dfrac{11}{4}\)

Dau bang xay ra khi x=3/2

Vay GTNN cua A=11/4 khi x=3/2

b) Ta co: x²-4x+6=(x-2)²+2≥2

=> B≥\(-\dfrac{5}{2}\)

Dấu bằng xảy ra khí : x=2

Vay GTNN cua B=-5/2 khi x=2

c) \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\ge\dfrac{9}{a+b+c}\left(bdt\right)\)

=> (a+b+c).\(\dfrac{9}{a+b+c}\ge9\)

Dau bang xay ra khi : a=b=c=1/3

Vay GTNN cua C=9 khi a=b=c=1/3

3.15=-6.x

=> -6x=45

=> x=-45/6=-9/2

sai.tick cho cả mình nưax nha

/x+1/=6+3+2x=9+2x

=> \(\left[{}\begin{matrix}x+1=9+2x\\x+1=-\left(9+2x\right)\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x+8=0\\3x=-10\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}x=-8\\x=-\dfrac{10}{3}\end{matrix}\right.\)

/x-1/=6+3+2x=9+2x

=> \(\left[{}\begin{matrix}x-1=9+2x\\x-1=-\left(9+2x\right)\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x+10=0\\3x=-8\end{matrix}\right.\)

=> \(\left[{}\begin{matrix}x=-10\\x=-\dfrac{8}{3}\end{matrix}\right.\)

(x³-x²)-(x-1)=0

=> x²(x-1)-(x-1)=0

=> (x²-1)(x-1)=0

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

=> (x-1)²(x+1)=0

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

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