Môn học: Toán Tiếng Anh Đề bài: Find a square number consists of 4 numbers knowing that the number consisting 2 first numbers is 1 unit greater than

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1. xin hay nhất

   

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2. Solution:

   $8281$

   Step by step solution:

   Let $\overline{abcd}$ be the giving square number.

   So it can be rewrite as $\overline{abcd}= k^2\quad (32 \leqslant k < 100)$

   Or: $1000a + 100b + 10c + d = k^2$

   In the other hand, we have:

   $\overline{ab} – \overline{cd}= 1$

   Or: $10a + b – (10c + d) = 1$

   Then we get:

   $1000a + 100b + 10c + d + 10a + b – (10c + d)= k^2 +1$

   It’s equal to: $\quad 1010a + 101b = k^2 + 1$

   Or: $\quad 101(10a + b) = k^2 + 1$

   It means: $\quad k^2 + 1\ \vdots\ 101$

   So that: $\quad k^2 + 101 – 100\ \vdots\ 101$

   Thus: $\quad k^2 – 100\ \vdots\ 101$

   Hence: $\quad (k-10)(k+10)\ \vdots\ 101$

   Because $\quad k – 10 < 101$

   Then: $\quad k + 10\ \vdots\ 101$

   Therefore: $\quad k = 91$

   We get: $\quad \overline{abcd}= 91^2 = 8281$

   Answer: $8281$

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