Question

a)x^2-4=(x-2)(x-3)

b)x^2-5x-6=0

c)x^2-7x+6=0

 

 

Answer 1

a: \(x^2-4=\left(x-2\right)\left(x-3\right)\)

=>\(\left(x-2\right)\left(x+2\right)-\left(x-2\right)\left(x-3\right)=0\)

=>\(\left(x-2\right)\left(x+2-x+3\right)=0\)

=>5(x-2)=0

=>x-2=0

=>x=2

b: \(x^2-5x-6=0\)

=>\(x^2-6x+x-6=0\)

=>(x-6)(x+1)=0

=>\(\left[{}\begin{matrix}x-6=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-1\end{matrix}\right.\)

c: \(x^2-7x+6=0\)

=>\(x^2-x-6x+6=0\)

=>x(x-1)-6(x-1)=0

=>(x-1)(x-6)=0

=>\(\left[{}\begin{matrix}x-1=0\\x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=6\end{matrix}\right.\)