Question

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請問這題怎麼用代數解法算？

7. 已知x為實數且|x+7=3|x-1|,求x之值。(x有兩解)
A:x=-1或x=5

高一數學 絕對值

Answer 1

✨ 最佳解答 ✨

綾

① x > 1
原式
=> x + 7 = 3(x - 1)
=> x = 5

② -7 < x < 1
原式
=> x + 7 = -3(x - 1)
=> x = -1

③ x < -7
原式
=> -(x + 7) = -3(x - 1)
=> x = 5 (-><-)

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謝謝！🤍

Answer 2

qn

平方
(x+7)² = [ 3(x-1) ] ²

(x²+14x+49)=9(x²-2x+1)

8x² - 32x - 40 = 0

x² - 4x - 5 = 0

(x-5)(x+1) = 0

x = 5 或 -1

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謝謝！🤍