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\(\sqrt{ab}\left(\sqrt{a}-\sqrt{b}\right)\)
\(\left(\sqrt{x}-\sqrt{y}\right)^2\)
\(x-1-2\sqrt{x-1}+1=\left(\sqrt{x-1}-1\right)^2\)
\(\left(\sqrt{15}x-4\right)^2\)
\(a\sqrt{a}-b\sqrt{b}\)
\(=\sqrt{a^3}-\sqrt{b^3}\)
\(=\left(\sqrt{a}-\sqrt{b}\right)\left(a+\sqrt{ab}+b\right)\)
\(x+y-2\sqrt{xy}\)
\(=\left(\sqrt{x}-\sqrt{y}\right)^2\)
\(xy-y\sqrt{x}+\sqrt{x}-1\)
\(=y\left(x-\sqrt{x}\right)+\left(\sqrt{x}-1\right)\)
\(=y\sqrt{x}\left(\sqrt{x}-1\right)+\left(\sqrt{x}-1\right)\)
\(\left(\sqrt{x}-1\right)\left(y\sqrt{x}+1\right)\)
Ta có : \(M=7\sqrt{x-1}-\sqrt{x^3-x^2}+x-1\)
\(=7\sqrt{x-1}-\sqrt{x^2\left(x-1\right)}+x-1\)
\(=7\sqrt{x-1}-x\sqrt{x-1}+\left(\sqrt{x-1}\right)^2\)
\(=\sqrt{x-1}\left(7-x+\sqrt{x-1}\right)\)
\(=\sqrt{x-1}\left(\sqrt{x-1}+2\right)\left(\sqrt{x-1}-3\right)\)
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, \(x-2\sqrt{x-1}\)
\(=\left(x-1\right)-2\sqrt{x-1}+1\)
\(=\left[\left(\sqrt{x-1}\right)-1\right]^2\)
\(M=7\sqrt{x-1}-\sqrt{x^2\left(x-1\right)}+\left(\sqrt{x-1}\right)^2=\sqrt{x-1}\left(7-x+\sqrt{x-1}\right)\)
\(=\sqrt{x-1}\left(6-\left(x-1\right)+\sqrt{x-1}\right)\)( đến đây bạn có thể đặt \(\sqrt{x-1}=t\),t>=0 rồi giải)
\(=-\sqrt{x-1}\left(\sqrt{x-1}-3\right)\left(\sqrt{x-1}+2\right)\)
Lời giải:
$x-2\sqrt{x}-15=(x-5\sqrt{x})+(3\sqrt{x}-15)$
$=\sqrt{x}(\sqrt{x}-5)+3(\sqrt{x}-5)=(\sqrt{x}-5)(\sqrt{x}+3)$
\(\text{ x - 2 √ x - 15}\)
\(=x+3\sqrt{x}\)\(-5\sqrt{x}\)\(-15\)
\(=\left(x+3\sqrt{x}\right)\)\(-\left(5\sqrt{x}\right)\)\(+15\)
\(=\sqrt{x}\)\(\left(\sqrt{x}+3\right)-5\left(\sqrt{x}+3\right)\)
\(\left(\sqrt{x}+3\right)-5\left(\sqrt{x}-5\right)\)