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Zefun
@Zefun
July 2022
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x+2/2+2/x+2=x+2/3+3/x+2 РЕшите задачу без дискриминанта(квадратное уровнение)
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ShirokovP
Verified answer
(x + 2)/2 + 2/(x + 2) = (x + 2)/3 + 3/(x + 2)
ОДЗ
x ≠ - 2
(x + 2)/2 + 2/(x + 2) - (x + 2)/3 - 3/(x + 2) = 0
3(x + 2)^2 + 12 - 2(x + 2)^2 - 18 = 0
(x + 2)^2 - 6 = 0
(x + 2)^2 = 6
x1 + 2 = √6
x2 + 2 = - √6
x1 = √6 - 2
x2 = - √6 - 2
Ответ
x1 = √6 - 2
x2 = - √6 - 2
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Answers & Comments
Verified answer
(x + 2)/2 + 2/(x + 2) = (x + 2)/3 + 3/(x + 2)ОДЗ
x ≠ - 2
(x + 2)/2 + 2/(x + 2) - (x + 2)/3 - 3/(x + 2) = 0
3(x + 2)^2 + 12 - 2(x + 2)^2 - 18 = 0
(x + 2)^2 - 6 = 0
(x + 2)^2 = 6
x1 + 2 = √6
x2 + 2 = - √6
x1 = √6 - 2
x2 = - √6 - 2
Ответ
x1 = √6 - 2
x2 = - √6 - 2