a) \(\left(y-1\right)^2=9\)
\(\Rightarrow\left(y-1\right)^2=3^2=\left(-3\right)^2\)
\(\Rightarrow x-1=3\Rightarrow x=4\)
\(\Rightarrow x-1=-3\Rightarrow x=-2\)
Vậy: \(x=4\) hoặc \(-2\)
\(\left(x-4\right)^2-25=0\)
\(\Rightarrow\left(x-4\right)^2=25\)
\(\Rightarrow\left(x-4\right)^2=5^2=\left(-5\right)^2\)
\(\Rightarrow x-4=5\Rightarrow x=9\)
\(\Rightarrow x-4=-5\Rightarrow x=-1\)
Vậy: \(x=9\) hoặc \(-1\)
\(\left(x-3\right)^2-\left(x-1\right)^2=0\)
\(\Rightarrow\left(x-3+x-1\right)\left(x-3-x+1\right)=0\)
\(\Rightarrow\left(x^2-4\right)\left(-2\right)=0\)
\(\Rightarrow x^2-4=0\)
\(\Rightarrow x^2=4\)
\(\Rightarrow x^2=2^2=\left(-2\right)^2\)
Mà: \(\left|-2-1\right|\ne\left|-2-3\right|\)
=> x = 2
\(\left(3x-7\right)^2-4\left(x+1\right)^2=0\)
\(\Rightarrow\left(3x-7\right)^2-\left(2x+2\right)^2=0\)
\(\Rightarrow\left(3x-7+2x+2\right)\left(3x-7-2x-2\right)=0\)
\(\Rightarrow\left(5x-5\right)\left(x-9\right)=0\)
\(\Rightarrow5x-5=0\Rightarrow x=1\)
\(\Rightarrow x-9=0\Rightarrow x=9\)
Vậy: x= 1 hoặc 9