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\(1.\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{\left(1+\sqrt{3}\right)^2}=\sqrt{\left(2-\sqrt{3}\right)^2}+\sqrt{\left(1+\sqrt{3}\right)^2}=2-\sqrt{3}+1+\sqrt{3}=3\) \(2a.\sqrt{x^2-2x+1}=7\)
⇔ \(x^2-2x+1=49\)
⇔ \(x^2-2x-48=0\)
⇔ \(\left(x+6\right)\left(x-8\right)=0\)
⇔ \(x=8orx=-6\)
\(b.\sqrt{4x-20}-3\sqrt{\dfrac{x-5}{9}}=\sqrt{1-x}\)
⇔ \(2\sqrt{x-5}-\sqrt{x-5}=\sqrt{1-x}\)
⇔ \(x-5=1-x\)
⇔ \(x=3\left(KTM\right)\)
KL.............
\(a.x+2\sqrt{x}=\sqrt{x}\left(\sqrt{x}+2\right)\)
\(b.x-\sqrt{x}=\sqrt{x}\left(\sqrt{x}-1\right)\)
\(c.x\sqrt{x}+x-\sqrt{x}-1=x\left(\sqrt{x}+1\right)-\left(\sqrt{x}+1\right)=\left(x-1\right)\left(\sqrt{x}+1\right)=\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2\)
\(d.a-\sqrt{ab}=\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)\)
\(e.x+2\sqrt{x}+1=\left(\sqrt{x}+1\right)^2=\left(\sqrt{x}+1\right)\left(\sqrt{x}+1\right)\)
\(f.x-4\sqrt{x}+4=\left(\sqrt{x}-2\right)^2=\left(\sqrt{x}-2\right)\left(\sqrt{x}-2\right)\)
\(g.x-4=\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)\)
\(h.a\sqrt{a}+b\sqrt{b}=\left(\sqrt{a}+\sqrt{b}\right)\left(a-\sqrt{ab}+b\right)\)
\(i.x\sqrt{x}-27=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)\)
\(k.x\sqrt{x}+1=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)
\(j.x^2-\sqrt{x}=\sqrt{x}\left(x\sqrt{x}-1\right)=\sqrt{x}\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\)
d: \(a-\sqrt{ab}=\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)\)
e: \(=\left(\sqrt{x}+1\right)^2\)
i: \(=\left(\sqrt{x}-3\right)\left(x+3\sqrt{x}+9\right)\)
k: \(=\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)\)