algebra · worked example

求解 x² - 25 = 0 — x = 5 or x = -5

解法:平方差。AI 验证的分步解答,免费使用。
Problem

x225=0x^2 - 25 = 0

分步解答

  1. 辨识为 a=xa = xb=5b = 5 的平方差。

  2. 应用 a2b2=(ab)(a+b)a^2 - b^2 = (a-b)(a+b)(x5)(x+5)=0(x - 5)(x + 5) = 0

  3. 令每个因式为零:x=5x = 5x=5x = -5

答案

x=5orx=5x = 5 \quad \text{or} \quad x = -5

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