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=7986575756465353578708806867463524243445568679988087685746353524132435645675 OK
99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999
Gọi số đó là \(\overline{xyz}\). Theo đề bài, ta có \(2\left(yz+5\right)=x^2\) \(\Rightarrow x⋮2\)
Mà \(2\left(yz+5\right)\ge10\) nên \(x^2\ge10\Leftrightarrow x\ge4\)
\(\Rightarrow x\in\left\{4,6,8\right\}\)
Nếu \(x=4\) thì \(yz+5=8\Leftrightarrow yz=3\) \(\Rightarrow\left(y,z\right)\in\left\{\left(1;3\right),\left(3;1\right)\right\}\)
Nếu \(x=6\) thì \(yz+5=18\Leftrightarrow yz=13\), vô lí.
Nếu \(x=8\) thì \(yz+5=32\Leftrightarrow yz=27\) \(\Leftrightarrow yz\in\left\{\left(3;9\right),\left(9;3\right)\right\}\)
Vậy có 4 số thỏa mãn ycbt là 413, 431, 839, 893.
Chọn C.
Theo tính chất của cấp số cộng và cấp số nhân ta có
Vậy |x-2y| = 6
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