76
a,x^2-25-(x+5)=0
<=>(x^2-5^2)-(x+5)=0
<=>(x+5)(x-5)(x+5)=0
<=>(x+5)(x-5+1)=0
<=>(x+5)(x-6)=0
<=>*x+5=0=>x=-5
*x-6=0=>x=6
76)
a) \(x^2-25-\left(x+5\right)=0\)
\(\Leftrightarrow\left(x^2-5^2\right)-\left(x+5\right)=0\)
\(\Leftrightarrow\left(x-5\right)\left(x+5\right)-\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-5-1\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(x-6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\x-6=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=6\end{matrix}\right.\)
Vậy x=-5 ; x=6
b) \(\left(2x-1\right)^2-\left(4x^2-1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)^2-\left[\left(2x\right)^2-1^2\right]=0\)
\(\Leftrightarrow\left(2x-1\right)^2-\left(2x-1\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left(2x-1\right)\left[2x-1-\left(2x+1\right)\right]=0\)
\(\Leftrightarrow\left(2x-1\right)\left(2x-1-2x-1\right)=0\)
\(\Leftrightarrow\left(-2\right)\left(2x-1\right)=0\)
\(\Leftrightarrow-4x+2=0\)
\(\Leftrightarrow-4x=-2\)
\(\Leftrightarrow x=\dfrac{-2}{-4}=\dfrac{1}{2}\)
Vậy \(x=\dfrac{1}{2}\)
c) \(x^2\left(x^2+4\right)-x^2-4=0\)
\(\Leftrightarrow x^2\left(x^2+4\right)-\left(x^2+4\right)=0\)
\(\Leftrightarrow\left(x^2+4\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x^2+4\right)\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+4=0\\x-1=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2=-4\left(loai\right)\\x=1\\x=-1\end{matrix}\right.\)
Vậy x=1 ; x=-1
