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aurum991
@aurum991
August 2022
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|x^2-x-5|+|x^2-x-9|=10
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Удачник66
Verified answer
Сделаем замену x^2-x-5 = y
|y| + |y-4| = 10
1) Если y <0, то y-4 <0
-y + 4 - y = 10
y = -3 < 0 - подходит
x^2-x-5 = -3
x^2-x-2 = 0
(x+1)(x-2) = 0
x1=-1; x2=2
2) Если 0 <= y < 4, то
y + 4 - y = 10
4 = 10
Решений нет
3) Если y >= 4, то
y + y - 4 = 10
y = 7 > 4 - подходит
x^2-x-5 = 7
x^2-x-12 = 0
(x-4)(x+3) = 0
x3 = -3; x4 = 4
Ответ: -3; -1; 2; 4
2 votes
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Answers & Comments
Verified answer
Сделаем замену x^2-x-5 = y|y| + |y-4| = 10
1) Если y <0, то y-4 <0
-y + 4 - y = 10
y = -3 < 0 - подходит
x^2-x-5 = -3
x^2-x-2 = 0
(x+1)(x-2) = 0
x1=-1; x2=2
2) Если 0 <= y < 4, то
y + 4 - y = 10
4 = 10
Решений нет
3) Если y >= 4, то
y + y - 4 = 10
y = 7 > 4 - подходит
x^2-x-5 = 7
x^2-x-12 = 0
(x-4)(x+3) = 0
x3 = -3; x4 = 4
Ответ: -3; -1; 2; 4