a ) \(\sqrt{12-2\sqrt{11}}-\sqrt{11}=\sqrt{11}-1-\sqrt{11}=-1\)
b ) \(x-4+\sqrt{16-8x+x^2}\left(x>4\right)\)
\(=x-4+x-4=-8\)
c ) \(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}=\sqrt{2}-1+\sqrt{2}+1=2\sqrt{2}\)
a,
\(\sqrt{12-2\sqrt{11}}-\sqrt{11}\\ =\sqrt{\left(\sqrt{11}-1\right)^2}-\sqrt{11}\\ =\left|\sqrt{11}-1\right|-\sqrt{11}\\ =\sqrt{11}-1-\sqrt{11}\\ =-1\)
b,
\(x-4+\sqrt{16-8x+x^2}\\ =x-4+\sqrt{\left(4-x\right)^2}\\ =x-4+\left|4-x\right|\\ =x-4+x-4\\ =2x-8\\ =2\left(x-4\right)\)
c,
\(\sqrt{3-2\sqrt{2}}+\sqrt{3+2\sqrt{2}}\\ =\sqrt{\left(\sqrt{2}-1\right)^2}+\sqrt{\left(\sqrt{2}+1\right)^2}\\ =\left|\sqrt{2}-1\right|+\left|\sqrt{2}+1\right|\\ =\sqrt{2}-1+\sqrt{2}+1\\ =2\sqrt{2}\)
d,
\(A=\dfrac{a\sqrt{a}-8+2a-4\sqrt{a}}{a-4}\\ =\dfrac{\left(a\sqrt{a}-4\sqrt{a}\right)+\left(2a-8\right)}{a-4}\\ =\dfrac{\left(a-4\right)\sqrt{a}+2\left(a-4\right)}{a-4}\\ =\dfrac{\left(a-4\right)\left(\sqrt{a}+2\right)}{\left(a-4\right)}\\ =\sqrt{a}+2\)