algebra · worked example

Solve x² - 25 = 0

Method: 平方差. Verified step-by-step solution with our free AI math solver.
Problem

x225=0x^2 - 25 = 0

Step-by-step solution

  1. 辨識為 a=xa = xb=5b = 5 的平方差。

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

  3. 令每個因式為零:x=5x = 5x=5x = -5

Answer

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

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