Question

bài 1
thu gọn biểu thức
a/(x+1)(x^2-x+1)-(x-1)(x^2+x+1)
b/2x^2-4x+2/2x-2
bài 2
phân thức đa thức thành nhân tử
a/x^2-4y^2+12y-9
b/5x^2+3(x+y)^2-5y^2
bài 3
tìm x biết
a/x^3-x+0
b/(3x+1)^2=x^2+2x+1
bài 4
cho a,b>0.tìm GTNN của A=(a+b)(1/a+1/b)

Answer 1

1.

a. \((x+1)(x^2-x+1)-(x-1)(x^2+x+1)\)

\(=x^3 + 1-(x^3-1) = 2 \)

b.

\(\dfrac{2x^2-4x+2}{2x-2}=\dfrac{2\left(x^2-2x+1\right)}{2\left(x-1\right)}=\dfrac{\left(x-1\right)^2}{x-1}=x-1\)

Answer 2

2.

a. \(x^2-4y^2+12y-9=x^2-\left[\left(2y\right)^2-2\cdot2y\cdot3+3^2\right]=x^2-\left(2y-3\right)^2=\left(x-2y+3\right)\left(x+2y-3\right)\)

b.

\(5x^2+3\left(x+y\right)^2-5y^2\)

\(=3\left(x+y\right)^2+5\left(x^2-y^2\right)\)

\(=3\left(x+y\right)^2+5\left(x+y\right)\left(x-y\right)\)

\(=\left(x+y\right)\left[3\left(x+y\right)+5\left(x-y\right)\right]\)

\(=\left(x+y\right)\left(3x+3y+5x-5y\right)\)

\(=\left(x+y\right)\left(8x-2y\right)=2\left(x+y\right)\left(4x-y\right)\)

Answer 3

3.

a.

\(x^3-x=0\)

\(\Leftrightarrow x\left(x^2-1\right)=0\)

\(\Leftrightarrow x\left(x+1\right)\left(x-1\right)\)

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

b.

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

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

\(\Leftrightarrow\left[{}\begin{matrix}3x+1=x+1\\3x+1=-x-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{1}{2}\end{matrix}\right.\)

Answer 4

\(A=\left(a+b\right)\left(\dfrac{1}{a}+\dfrac{1}{b}\right)=1+\dfrac{a}{b}+\dfrac{b}{a}+1\)

\(=2+\left(\dfrac{a}{b}+\dfrac{b}{a}\right)\ge2+2\sqrt{\dfrac{a}{b}\cdot\dfrac{b}{a}}=2+2=4\)

Dấu "=" khi a = b