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|A| = |B| の絶対値を外した時、考えられる式は、
① A = B
② A = -B
③ -A = B
④ -A = -B
の4つです。

ここで、①と④、②と③は同じことを指すので、結局、A = B ・ A = -B
つまり、A = ±B が言えるのです。

ありがとうございます‼︎

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