Задание 7, стр 60

Выберите один из известных вам методов и решите уравнение.
1)t2 + 8t + 15 = 0
2) p2 + 4p + 1 = 0
3)2a2 + 4a + 1 = 0
4)m2 + 6m + 8 = 0
5)q2 + 2q + 1 = 0
6)3a2 + 6a − 3 = 0
7)t2 − 2∕5t = 0
8)n(n − 4) = n
9)n2 −2 3n = 8 9

Answers

1)
t2 + 8t + 15 = 0
t2 + 8t + 16 − 1 = 0
(t + 4)2 = 1
t + 4 = 1;t + 4 = −1
t1 = −3;t2 = −5
Ответ: -3; -5
2)
p2 + 4p + 1 = 0
D = 16 − 4 = 12
p1 = (−4 + 12)2 = −2 + 3
p2 = (−4 −12)2 = −2 −3
Ответ: 2 −3;2 + 3
3)
2a2 + 4a + 1 = 7
2a2 + 4a − 6 = 0
a2 + 2a − 3 = 0
a2 + 2a + 1 − 4 = 0
(a + 1)2 = 4
a + 1 = 2;a + 1 = −2
a1 = 1a2 = −3
Ответ: 1; -3
4)
m2 + 6m + 8 = 0
(m + 3)2 = 1
m + 3 = −1m + 3 = 1
m1 = −4m2 = −2
Ответ:-4; -2
5)
q2 + 2q + 1 = 0
(q + 1)2 = 0
q + 1 = 0
q = −1
Ответ: − 1
6)
3a2 + 6a − 3 = 0
a2 + 2a − 1 = 0
D = 4 + 4 = 8
a1 = (−2 + 8)2 = −1 + 2
a2 = (−2 −8)2 = −1 −2
Ответ: − 1 + 2;−1 −2
7)
t2 −2 5t = 0
5t2 − 2t = 0
t(5t − 2) = 0
t1 = 05t − 2 = 0
t2 = 0,4
Ответ: 0;0,4
8)
n(n − 4) = n
n2 − 4n − n = 0
n2 − 5n = 0
n(n − 5) = 0
n = 0n = 5

Ответ:0; 5

9)
n2 −2 3n = 8 9
9n2 − 6n − 8 = 0
D = 36 + 496 = 324 = 182
x1 = (6 + 18)18 = 4 3
x2 = (6 − 18)18 = −2 3
Ответ: 4 3; −2 3 .
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2022-10-21 06:59
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