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kolosnyusha
@kolosnyusha
July 2022
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x(x+3)(x+5)(x+8)=100
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ShirokovP
Verified answer
Сгруппируем таким образом:
x (x + 8)(x + 3)(x + 5) = 100
(x^2 + 8x)(x^2 + 8x + 15) = 100
Пусть t = x^2 + 8x, тогда t(t + 15) = 100
t^2 + 15t = 100
t^2 + 15t - 100 = 0
D = 625 = 25^2
t1 = ( - 15 + 25)/2 = 5;
t2 = ( - 15 - 25)/2 = - 20;
1)
x^2 + 8x = 5
x^2 + 8x - 5 = 0
D = 64 + 4*5 = 64 + 20 = 84
√D = 2√21
x1 = ( - 8 + 2√21)/2 = - 4 + √21;
x2 = ( - 8 - 2√21)/2 = - 4 - √21;
2)
x^2 + 8x = - 20
x^2 + 8x + 20 = 0
D = 64 - 4*20 = 64 - 80 = - 16 < 0
нет решений
Ответ:
- 4 + √21;
- 4 - √21;
16 votes
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Answers & Comments
Verified answer
Сгруппируем таким образом:x (x + 8)(x + 3)(x + 5) = 100
(x^2 + 8x)(x^2 + 8x + 15) = 100
Пусть t = x^2 + 8x, тогда t(t + 15) = 100
t^2 + 15t = 100
t^2 + 15t - 100 = 0
D = 625 = 25^2
t1 = ( - 15 + 25)/2 = 5;
t2 = ( - 15 - 25)/2 = - 20;
1)
x^2 + 8x = 5
x^2 + 8x - 5 = 0
D = 64 + 4*5 = 64 + 20 = 84
√D = 2√21
x1 = ( - 8 + 2√21)/2 = - 4 + √21;
x2 = ( - 8 - 2√21)/2 = - 4 - √21;
2)
x^2 + 8x = - 20
x^2 + 8x + 20 = 0
D = 64 - 4*20 = 64 - 80 = - 16 < 0
нет решений
Ответ:
- 4 + √21;
- 4 - √21;