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\(\sqrt{x}+\sqrt{y}+\sqrt{xy}+1\)
\(=\sqrt{x}+\sqrt{y}+\sqrt{x}.\sqrt{y}+1\)
\(=\sqrt{x}\left(\sqrt{y}+1\right)+\left(\sqrt{y}+1\right)\)
\(=\left(\sqrt{x}+1\right)\left(\sqrt{y}+1\right)\)
a: \(=9\sqrt{2}-4\sqrt{2}+4\sqrt{2}+9\sqrt{2}=18\sqrt{2}\)
b: \(=8\sqrt{3}-12\sqrt{3}+5\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)
c: \(=2\sqrt{21}\)
Bài 2 :
a) \(A=\sqrt{8+2\sqrt{7}}-\sqrt{7}=\sqrt{7+2\sqrt{7}+1}-\sqrt{7}\)
\(=\sqrt{\left(\sqrt{7}+1\right)^2}-\sqrt{7}=\left|\sqrt{7}+1\right|-\sqrt{7}=\sqrt{7}+1-\sqrt{7}=1\)
b) \(B=\sqrt{7+4\sqrt{3}}-2\sqrt{3}=\sqrt{4+4\sqrt{3}+3}-2\sqrt{3}\)
\(=\sqrt{\left(2+\sqrt{3}\right)^2}-2\sqrt{3}=\left|2+\sqrt{3}\right|-2\sqrt{3}\)
\(=2+\sqrt{3}-2\sqrt{3}=2-\sqrt{3}\)
c) \(C=\sqrt{14-2\sqrt{13}}+\sqrt{14+2\sqrt{13}}\)
\(=\sqrt{13-2\sqrt{13}+1}+\sqrt{13+2\sqrt{13}+1}\)
\(=\sqrt{\left(\sqrt{13}-1\right)^2}+\sqrt{\left(\sqrt{13}+1\right)^2}\)
\(=\left|\sqrt{13}-1\right|+\left|\sqrt{13}+1\right|\)
\(=\sqrt{13}-1+\sqrt{13}+1=2\sqrt{13}\)
d) \(D=\sqrt{22-2\sqrt{21}}+\sqrt{22+2\sqrt{21}}\)
\(=\sqrt{21-2\sqrt{21}+1}+\sqrt{21+2\sqrt{21}+1}\)
\(=\sqrt{\left(\sqrt{21}-1\right)^2}+\sqrt{\left(\sqrt{21}+1\right)^2}\)
\(=\left|\sqrt{21}-1\right|+\left|\sqrt{21}+1\right|\)
\(=\sqrt{21}-1+\sqrt{21}+1=2\sqrt{21}\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
\(\sqrt{ab}-\sqrt{a}-\sqrt{b}+1\)
\(=\left(\sqrt{ab}-\sqrt{a}\right)-\left(\sqrt{b}-1\right)\)
\(=\sqrt{a}\left(\sqrt{b}-1\right)-\left(\sqrt{b}-1\right)\)
\(=\left(\sqrt{b}-1\right)\left(\sqrt{a}-1\right)\)
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