Bài 4:
1: \(x^2+y^2+4y+13=6x\)
=>\(x^2-6x+9+y^2+4y+4=0\)
=>\(\left(x-3\right)^2+\left(y+2\right)^2=0\)
=>\(\begin{cases}x-3=0\\ y+2=0\end{cases}\Rightarrow\begin{cases}x=3\\ y=-2\end{cases}\)
2: \(x^2+y^2+17=2x-8y\)
=>\(x^2-2x+1+y^2+8y+16=0\)
=>\(\left(x-1\right)^2+\left(y+4\right)^2=0\)
=>\(\begin{cases}x-1=0\\ y+4=0\end{cases}\Rightarrow\begin{cases}x=1\\ y=-4\end{cases}\)
Bài 3:
1: \(4x^2-4=0\)
=>\(4x^2=4\)
=>\(x^2=1\)
=>\(\left[\begin{array}{l}x=1\\ x=-1\end{array}\right.\)
2: \(4x^2-36=0\)
=>\(4x^2=36\)
=>\(x^2=9\)
=>\(\left[\begin{array}{l}x=3\\ x=-3\end{array}\right.\)
3: \(4x^2-36=0\)
=>\(4\left(x^2-9\right)=0\)
=>4(x-3)(x+3)=0
=>(x-3)(x+3)=0
=>\(\left[\begin{array}{l}x-3=0\\ x+3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=3\\ x=-3\end{array}\right.\)
4: \(\left(3x+1\right)^2-16=0\)
=>(3x+1+4)(3x+1-4)=0
=>(3x+5)(3x-3)=0
=>\(\left[\begin{array}{l}3x+5=0\\ 3x-3=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=-\frac53\\ x=1\end{array}\right.\)
5: \(\left(2x-3\right)^2-49=0\)
=>(2x-3-7)(2x-3+7)=0
=>(2x-10)(2x+4)=0
=>\(2\left(x-5\right)\cdot2\left(x+2\right)=0\)
=>(x-5)(x+2)=0
=>\(\left[\begin{array}{l}x-5=0\\ x+2=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\\ x=-2\end{array}\right.\)
6: \(\left(2x-5\right)^2-x^2=0\)
=>(2x-5-x)(2x-5+x)=0
=>(x-5)(3x-5)=0
=>\(\left[\begin{array}{l}x-5=0\\ 3x-5=0\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\\ 3x=5\end{array}\right.\Rightarrow\left[\begin{array}{l}x=5\\ x=\frac53\end{array}\right.\)
Bài 2:
1: \(x\left(1-x\right)+\left(x-1\right)^2\)
\(=x-x^2+x^2-2x+1\)
=-x+1
2: \(\left(x-3\right)^2-x^2+10x-7\)
\(=x^2-6x+9-x^2+10x-7\)
=4x+2
3: \(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\)
\(=x^2+4x+4-\left(x^2+x-3x-3\right)\)
\(=x^2+4x+4-\left(x^2-2x-3\right)\)
\(=x^2+4x+4-x^2+2x+3=6x+7\)
4: \(\left(x+4\right)\left(x-2\right)-\left(x-3\right)^2\)
\(=x^2-2x+4x-8-\left(x^2-6x+9\right)\)
\(=x^2+2x-8-x^2+6x-9=8x-17\)
Bài 1:
1: \(\left(5x+1\right)^2=\left(5x\right)^2+2\cdot5x\cdot1=25x^2+10x+1\)
2: \(\left(2x+3\right)^2=\left(2x\right)^2+2\cdot2x\cdot3+3^2=4x^2+12x+9\)
3: \(\left(2x-1\right)^2=\left(2x\right)^2-2\cdot2x\cdot1+1^2=4x^2-4x+1\)
4: \(\left(3x-2\right)^2=\left(3x\right)^2-2\cdot3x\cdot2+2^2=9x^2-12x+4\)
5: \(\left(x+2y\right)^2=x^2+2\cdot x\cdot2y+\left(2y\right)^2=x^2+4xy+4y^2\)
6: \(\left(x+5y\right)^2=x^2+2\cdot x\cdot5y+\left(5y\right)^2=x^2+10xy+25y^2\)
7: \(\left(x-2y\right)^2=x^2-2\cdot x\cdot2y+\left(2y\right)^2=x^2-4xy+4y^2\)
8: \(\left(2x-y\right)^2=\left(2x\right)^2-2\cdot2x\cdot y+y^2=4x^2-4xy+y^2\)
