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a, \(x^2-7=x^2-\left(\sqrt{7}\right)^2=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)
b, \(x^2-2\sqrt{2}x+2=x^2-2\sqrt{2}x+\left(\sqrt{2}\right)^2=\left(x-\sqrt{2}\right)^2\)
c, \(x^2+2\sqrt{13}x+13=x^2+2\sqrt{13}x+\left(\sqrt{13}\right)^2=\left(x+\sqrt{13}\right)^2\)
a) \(x^2-7=x^2-\left(\sqrt{7}\right)^2=\left(x-\sqrt{7}\right)\left(x+\sqrt{7}\right)\)
b) \(x^2-2\sqrt{2}x+2=x^2-2.x.\sqrt{2}+\left(\sqrt{2}\right)^2=\left(x-\sqrt{2}\right)^2\)
c) \(x^2+2\sqrt{13}x+13=x^2+2.x.\sqrt{13}+\left(\sqrt{13}\right)^2=\left(x+\sqrt{13}\right)^2\)
\(\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
\(\left(\sqrt{x}-\sqrt{y}\right)^2\)
\(x-1-2\sqrt{x-1}+1=\left(\sqrt{x-1}-1\right)^2\)
\(\left(\sqrt{15}x-4\right)^2\)
\(a\sqrt{a}-b\sqrt{b}\)
\(=\sqrt{a^3}-\sqrt{b^3}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)\)
\(x+y-2\sqrt{xy}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2\)
1/ \(x-6\sqrt{x}-8=\left(\sqrt{x}-3+\sqrt{17}\right)\left(\sqrt{x}-3-\sqrt{17}\right)\)
2/ Bài này làm gì còn phân tích được nữa.
a, \(x-\sqrt{x}\)= \(\sqrt{x}.\left(\sqrt{x}-1\right)\)
b, 3x+6\(\sqrt{x}\)= \(\sqrt{x}.\left(3\sqrt{x}+6\right)\)
c, x+2\(\sqrt{x}+1\)= \(\left(\sqrt{x}\right)^2+2\sqrt{x}+1=\left(\sqrt{x}+1\right)^2\)
d, \(3x-5\sqrt{x}+2=3x-3\sqrt{x}-2\sqrt{x}+2\)
=\(3\sqrt{x}.\left(\sqrt{x}-1\right)-2.\left(\sqrt{x}-1\right)\)
=\(\left(3\sqrt{x}-2\right).\left(\sqrt{x}-1\right)\)
\(-\sqrt{x}+x-2\)
\(=x-\sqrt{x}-2=x+\sqrt{x}-2\sqrt{x}-2\)
\(=\sqrt{x}\left(\sqrt{x}+1\right)-2\left(\sqrt{x}+1\right)\)
\(=\left(\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
a, \(1-a\sqrt{a}\)
\(=\left[1-\left(\sqrt{a}\right)^3\right]\)
\(=\left(1-\sqrt{a}\right)\left[\left(\sqrt{a}\right)^2+1.\sqrt{a}+1^2\right]\)
\(=\left(1-\sqrt{a}\right)\left(a+\sqrt{a}+1\right)\)
b, \(x-2\sqrt{x-1}\)
\(=\left(x-1\right)-2\sqrt{x-1}+1\)
\(=\left[\left(\sqrt{x-1}\right)-1\right]^2\)
\(=\left(x+\sqrt{2}\right)^2\)
(x+√2)^2