Question

1. Tìm x:

a) (3x-1)^2=(x-2)^2

b) 5x^2 -4.(x^2-2x+1)-5=0

2. Phân tích:

a) x^3+x^2y-x^2z-xyz

b) x^2+2xy+3x+y^2-3y

c)4y^3-1/16

5. C/m: 8^7-2^18 chia hết cho 14

6. CMR: Hiệu các bình phương 2 số lẻ liên tiếp thì chia hết cho 8.

( các bạn giúp mình nhé, mình cần hơi gấp 😶😊)

Answer 1

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

⇔\(9x^2-6x+1=x^2-4x+4\)

\(\Leftrightarrow8x^2-2x-3=0\)

\(\Leftrightarrow8x^2-6x+4x-3=0\)

\(\Leftrightarrow\left(2x+1\right)\left(4x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+1=0\\4x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\frac{-1}{2}\\x=\frac{3}{4}\end{matrix}\right.\)

Answer 2

\(5x^2-4\left(x^2-2x+1\right)-5=0\)

\(\Leftrightarrow x^2+8x-9=0\)

\(\Leftrightarrow\left(x-1\right)\left(x+9\right)=0\)

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

Answer 3

\(x^3+x^2y-x^2z-xyz=x^2\left(x+y\right)-xz\left(x+y\right)\)

\(=x\left(x-z\right)\left(x+y\right)\)