\(a,\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=6\)
\(\Rightarrow x^2-4x+4-x^2+9=6\)
\(\Rightarrow-4x+13=6\)
\(\Rightarrow x=\dfrac{6-13}{-4}=\dfrac{7}{4}\)
\(b,4\left(x-3\right)^2-\left(2x-1\right)\left(2x+1\right)=10\)
\(\Rightarrow4\left(x^2-6x+9\right)-4x^2+1=10\)
\(\Rightarrow4x^2-24x+36-4x^2+1=10\)
\(\Rightarrow-24x+37=10\)
\(\Rightarrow x=\dfrac{10-37}{-24}=\dfrac{27}{24}\)
\(c,x^2-16-3\left(x+4\right)=0\)
\(\Rightarrow x^2-16-3x-12=0\)
\(\Rightarrow x^2-3x-28=0\)
\(\Rightarrow x^2-7x+4x-28=0\)
\(\Rightarrow\left(x-7\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\x+4=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=7\\x=-4\end{matrix}\right.\)
\(d,\left(x-4\right)^2-\left(x-2\right)\left(x+2\right)=6\)
\(\Rightarrow x^2-8x+16-x^2+4=6\)
\(\Rightarrow-8x+20=6\)
\(\Rightarrow x=\dfrac{6-20}{-8}=\dfrac{-14}{-8}=\dfrac{7}{4}\)
\(e,9\left(x+1\right)^2-\left(3x-2\right)\left(3x+2\right)=10\)
\(\Rightarrow9x^2+18x+9-9x^2+4=10\)
\(\Rightarrow18x+13=10\)
\(\Rightarrow x=\dfrac{10-13}{18}=\dfrac{-3}{18}=\dfrac{-1}{6}\)
a, (x-2)^2-(x-3)(x+3)=6
=> x2-4x+4-(x2-9)=6
=> x2-4x+4-x2+9-6=0
=> -4x+7=0
=> -4x=-7
=> x=\(\dfrac{7}{4}\)