c: \(x^2-6\sqrt{x^2+5}+x=2\sqrt{x-1}-14\)
=>\(x^2-4-6\left(\sqrt{x^2+5}-3\right)+x-2-2\sqrt{x-1}+2=0\)
=>\(\left(x-2\right)\left(x+2\right)-6\cdot\dfrac{x^2+5-9}{\sqrt{x^2+5}+3}+\left(x-2\right)-2\cdot\dfrac{x-1-1}{\sqrt{x-1}+1}=0\)
=>\(\left(x-2\right)\left(x+2\right)-\dfrac{6}{\sqrt{x^2+5}+3}\cdot\left(x-2\right)\left(x+2\right)+\left(x-2\right)-2\cdot\dfrac{x-2}{\sqrt{x-1}+1}=0\)
=>\(\left(x-2\right)\left[\left(x+2\right)-\dfrac{6}{\sqrt{x^2+5}+3}\cdot\left(x+2\right)+1-\dfrac{2}{\sqrt{x-1}+1}\right]=0\)
=>x-2=0
=>x=2
d: \(x^2-\sqrt{\left(x^2-8\right)\left(x-2\right)}+x=\sqrt{x^2-8}+\sqrt{x-2}+9\)
=>\(x^2-9-\sqrt{\left(x^2-8\right)\left(x-2\right)}+x-\sqrt{x^2-8}-\sqrt{x-2}=0\)
=>\(\Leftrightarrow\left(x-3\right)\left(x+3\right)-\sqrt{x^3-2x^2-8x+16}+x-3+1-\sqrt{x^2-8}+2-\sqrt{x-2}=0\)
=>\(\left(x-3\right)\left(x+3\right)+\left(x-3\right)-\sqrt{x^3-2x^2-8x+16}+1+\dfrac{1-x^2+8}{1+\sqrt{x^2-8}}+1-\sqrt{x-2}=0\)
=>\(\left(x-3\right)\left(x+4\right)-\dfrac{x^3-2x^2-8x+16-1}{\sqrt{x^3-2x^2-8x+16}+1}-\dfrac{\left(x-3\right)\left(x+3\right)}{\sqrt{x^2-8}+1}+\dfrac{1-x+2}{1+\sqrt{x-2}}=0\)
=>\(\left(x-3\right)\left(x+4\right)-\dfrac{x^3-2x^2-8x+15}{\sqrt{x^3-2x^2-8x+16}+1}-\dfrac{\left(x-3\right)\left(x+3\right)}{\sqrt{x^2-8}+1}-\dfrac{x-3}{1+\sqrt{x-2}}=0\)
\(\Leftrightarrow\left(x-3\right)\left(x+4\right)-\dfrac{\left(x-3\right)\left(x^2+x-5\right)}{\sqrt{x^3-2x^2-8x+16}+1}-\dfrac{\left(x-3\right)\left(x+3\right)}{\sqrt{x^2-8}+1}-\dfrac{x-3}{1+\sqrt{x-2}}=0\)
\(\Leftrightarrow\left(x-3\right)\left[\left(x+4\right)-\dfrac{x^2+x-5}{\sqrt{x^3-2x^2-8x+16}+1}-\dfrac{x+3}{\sqrt{x^2-8}+1}-\dfrac{1}{\sqrt{x-2}+1}\right]=0\)
=>x-3=0
=>x=3
