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littlemuffin
@littlemuffin
August 2022
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решите уравнение 4/(x-9)+9/(x-4)=2
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ShirokovP
Verified answer
ОДЗ
x ≠ 9; x ≠ 4
4(x - 4) + 9(x - 9) = 2(x - 4)(x - 9)
4x - 16 + 9x - 81 = 2(x^2 - 13x + 36)
13x - 97 = 2x^2 - 26x + 72
2x^2 - 26x + 72 - 13x + 97 = 0
2x^2 - 39x + 169 = 0
D = 169 = 13^2
x1 = ( 39 + 13)/4 = 13
x2 = (39 - 13)/4 = 6,5
Ответ
6,5; 13
3 votes
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Answers & Comments
Verified answer
ОДЗx ≠ 9; x ≠ 4
4(x - 4) + 9(x - 9) = 2(x - 4)(x - 9)
4x - 16 + 9x - 81 = 2(x^2 - 13x + 36)
13x - 97 = 2x^2 - 26x + 72
2x^2 - 26x + 72 - 13x + 97 = 0
2x^2 - 39x + 169 = 0
D = 169 = 13^2
x1 = ( 39 + 13)/4 = 13
x2 = (39 - 13)/4 = 6,5
Ответ
6,5; 13