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\(P=\dfrac{20\left(x^2+6x+9\right)}{\left(3x+5+2x\right)\left(3x+5-2x\right)}+\dfrac{5\left(x-5\right)\left(x+5\right)}{\left(3x-2x-5\right)\left(3x+2x+5\right)}-\dfrac{\left(2x+3+x\right)\left(2x+3-x\right)}{3\left(x+3\right)\left(x+5\right)}\)
\(=\dfrac{20\left(x+3\right)^2}{5\left(x+1\right)\left(x+5\right)}+\dfrac{5\left(x-5\right)\left(x+5\right)}{\left(x-5\right)\cdot5\left(x+1\right)}-\dfrac{3\left(x+1\right)\left(x+3\right)}{3\left(x+3\right)\left(x+5\right)}\)
\(=\dfrac{5\left(x+3\right)^2}{\left(x+1\right)\left(x+5\right)}+\dfrac{\left(x+5\right)}{x+1}-\dfrac{x+1}{x+5}\)
\(=\dfrac{5x^2+30x+45+x^2+10x+25-x^2-2x-1}{\left(x+5\right)\left(x+1\right)}\)
\(=\dfrac{5x^2+38x+69}{\left(x+5\right)\left(x+1\right)}\)
\(=\dfrac{5x^2+38x+69}{x^2+6x+5}\)
Để P là số nguyên thì \(5x^2+30x+25+8x+34⋮x^2+6x+5\)
=>\(8x+34⋮x^2+6x+5\)
=>\(\left\{{}\begin{matrix}8x+34⋮x+1\\8x+34⋮x+5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}8x+8+26⋮x+1\\8x+40-6⋮x+5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x+1\in\left\{1;-1;2;-2;13;-13;26;-26\right\}\\x+5\in\left\{1;-1;2;-2;3;-3;6;-6\right\}\end{matrix}\right.\)
=>\(x\in\left\{-2;1\right\}\)
b \(P=\dfrac{\sqrt{x}+\sqrt{x}+2}{x-4}\cdot\dfrac{\sqrt{x}-2}{2}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
a: Khi x=64 thì \(P=\dfrac{8+1}{8+2}=\dfrac{9}{10}\)
b: \(P=\dfrac{\sqrt{x}+\sqrt{x}+2}{x-4}\cdot\dfrac{\sqrt{x}-2}{2}=\dfrac{\sqrt{x}+1}{\sqrt{x}+2}\)
a: Khi x=64 thì \(P=\dfrac{8+1}{8+2}=\dfrac{9}{10}\)
de A nguyen
=> 3 chia het cho \(\sqrt{x}-2\)
=> \(\sqrt{x}-2\in\left\{-3;-1;1;3\right\}\)
=>\(\sqrt{x}\in\left\{-1;1;3;5\right\}\)
=>x{1;1,73;1,2,23}
mình làm tròn số đấy
\(A\inℤ\Leftrightarrow3⋮\left(\sqrt{x}-2\right)\)
\(\Leftrightarrow\sqrt{x}-2\inƯ\left(3\right)=\left\{\pm1;\pm3\right\}\)
Lập bảng:
| \(\sqrt{x}-2\) | \(1\) | \(-1\) | \(3\) | \(-3\) |
| \(\sqrt{x}\) | \(3\) | \(1\) | \(5\) | \(-1\) |
| \(x\) | \(9\) | \(1\) | \(25\) | Loại vì \(\sqrt{x}\ge0\) |
Vậy \(x\in\left\{1;9;25\right\}\)
x có đk j k bạn