Toán Lớp 9: Q=(1/ √a+1-1/a+ √a): √a-1/a+2 √a+1.
Tìm a ngyên để Q nguyên.
Mn giúp mk vs.Tối nay mk cần rồi.
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Toán Lớp 9: Q=(1/ √a+1-1/a+ √a): √a-1/a+2 √a+1.
Tìm a ngyên để Q nguyên.
Mn giúp mk vs.Tối nay mk cần rồi.
Comments ( 1 )
DK:a \ge 0;a \ne 1\\
Q = \left( {\dfrac{1}{{\sqrt a + 1}} – \dfrac{1}{{a + \sqrt a }}} \right):\dfrac{{\sqrt a – 1}}{{a + 2\sqrt a + 1}}\\
= \dfrac{{\sqrt a – 1}}{{\sqrt a \left( {\sqrt a + 1} \right)}}.\dfrac{{{{\left( {\sqrt a + 1} \right)}^2}}}{{\sqrt a – 1}}\\
= \dfrac{{\sqrt a + 1}}{{\sqrt a }} = 1 + \dfrac{1}{{\sqrt a }}\\
Q \in Z \to \dfrac{1}{{\sqrt a }} \in Z\\
\to \sqrt a \in U\left( 1 \right)\\
\to \sqrt a = 1\\
\to a = 1\left( l \right)\\
\to a \in \emptyset
\end{array}\)