國中教甄｜資訊科技資訊科技109 年第 69 題單選題

A positional numeral system use 'X' as its radix. In this system, number 252 equals decimal number 209 as following equation: $25 2_{(x)} = 20 9_{(10)}$ . What is the value of 'X'?

D9正確答案

答案與詳解

正確答案

將 X 進位的 252 依位權展開為十進位方程式

2 X^{2} + 5 X + 2 = 209

，解得 X 為 9。

代入 X=9 計算得 $2 \times 9^{2} + 5 \times 9 + 2 = 162 + 45 + 2 = 209$ ，完全符合題意。

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A positional numeral system use 'X' as its radix. In this system, number 252 equals decimal number 209 as following equation: 252(x)​=209(10)​ . What is the value of 'X'?