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a, \(x^2-3=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)
b, \(x^2-6=\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)
c, \(x^2+2\sqrt{3}+3=x^2+2\sqrt{3}+\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)^2\)
d, \(x^2-2\sqrt{5}x+5=x^2-2\sqrt{5}x+\left(\sqrt{5}\right)^2=\left(x-\sqrt{5}\right)^2\)
a) \(x^2\) - 3 = (x-\(\sqrt{3}\))(x+\(\sqrt{3}\))
b)\(x^2\)-6=(x-\(\sqrt{6}\))(x+\(\sqrt{6}\))
c) \(x^2+2\sqrt{3}x+3\)= \(\left(x+\sqrt{3}\right)^2\)
d) \(x^2-2\sqrt{5}x+5\)=\(\left(x-\sqrt{5}\right)^2\)
2) a) \(x^2-3=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)
b) \(x^2-6=\left(x-\sqrt{6}\right).\left(x+\sqrt{6}\right)\)
c) = \(x^2+2x.\sqrt{3}+\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)^2\)
d) = \(x^2-2x\sqrt{5}+\left(\sqrt{5}\right)^2=\left(x-\sqrt{5}\right)^2\)
a, \(5+\sqrt{5}=\sqrt{5}\left(\sqrt{5}+1\right)\)
b, \(a-2\sqrt{a}=\sqrt{a}\left(\sqrt{a}-2\right)\)
c, \(x-\sqrt{xy}=\sqrt{x}\left(\sqrt{x}-\sqrt{y}\right)\)
d, \(x-y-\sqrt{x}-\sqrt{y}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)\left(\sqrt{x}+\sqrt{y}\right)-\left(\sqrt{x}+\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}-1\right)\)
\(A,ĐKXĐ:x;y\ge0\)
\(A=\sqrt{xy}-2\sqrt{y}-5\sqrt{x}+10\)
\(=\sqrt{y}\left(\sqrt{x}-2\right)-5\left(\sqrt{x}-2\right)\)
\(=\left(\sqrt{x}-2\right)\left(\sqrt{y}-5\right)\)
\(ĐKXĐ:x;y\ge0\)
\(B=a\sqrt{x}+b\sqrt{y}-\sqrt{xy}-ab\)
\(=\left(a\sqrt{x}-\sqrt{xy}\right)+\left(b\sqrt{y}-ab\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)+b\left(\sqrt{y}-a\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\sqrt{x}\left(a-\sqrt{y}\right)-b\left(a-\sqrt{y}\right)\)
\(=\left(a-\sqrt{y}\right)\left(\sqrt{x}-b\right)\)
a ) x 2 - 3 = x 2 - ( √ 3 ) 2 = ( x - √ 3 ) ( x + √ 3 ) b ) x 2 - 6 = x 2 - ( √ 6 ) 2 = ( x - √ 6 ) ( x + √ 6 ) c ) x 2 + 2 √ 3 x + 3 = x 2 + 2 √ 3 x + ( √ 3 ) 2 = ( x + √ 3 ) 2 d ) x 2 - 2 √ 5 x + 5 = x 2 - 2 √ 5 x + ( √ 5 ) 2 = ( x - √ 5 ) 2