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kate6777
@kate6777
December 2021
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ира250
A = log(12) (18) = log(2) (18) / log(2) (12) =
(log(2) (2) + log(2) (9)) / (log(2) (4) + log(2) (3)) = (1 + 2*log(2) (3)) / (2 + log(2) (3))
выразим отсюда log(2) (3)...
2a + a*log(2) (3) = 1 + 2*log(2) (3)
2a - 1 = (2-a) * log(2) (3)
log(2) (3) = (2a-1) / (2-a)
log(8) (9) = (1/3) * log(2) (9) = (2/3) * log(2) (3) = 2*(2a-1) / (3*(2-a)) = (4a-2) / (6-3a)
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Verified answer
№7
√3х²+7х-4=-х
(√3х²+7х-4)²=(-х)²
3х²+7х-4=х²
3х²+7х-4-х²=0
2х²+7х-4=0
Д=(7)²-4*2*(-4)=49++32=81>0 имеет два корня.
х₁=-7+√81\2*2=-7+9\4=2\4=0,5
х₂=-7-√81\2*2=-7-9\4=-16\4=-4
Проверка:
х₁=0,5
√3х²+7х-4=-х
√3*(0,5)²+7*0,5-4=-0,5
√0,75+3,5-4=-0,5
√0,25=-0,5
0,5≠-0,5
х₁=0,5- не является корнем уравнения.
х₂=-4
√3*(-4)²+7*(-4)-4=-(-4)
√48-28-4=4
√16=4
4=4
Ответ : х=-4.
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Answers & Comments
(log(2) (2) + log(2) (9)) / (log(2) (4) + log(2) (3)) = (1 + 2*log(2) (3)) / (2 + log(2) (3))
выразим отсюда log(2) (3)...
2a + a*log(2) (3) = 1 + 2*log(2) (3)
2a - 1 = (2-a) * log(2) (3)
log(2) (3) = (2a-1) / (2-a)
log(8) (9) = (1/3) * log(2) (9) = (2/3) * log(2) (3) = 2*(2a-1) / (3*(2-a)) = (4a-2) / (6-3a)
Verified answer
№7√3х²+7х-4=-х
(√3х²+7х-4)²=(-х)²
3х²+7х-4=х²
3х²+7х-4-х²=0
2х²+7х-4=0
Д=(7)²-4*2*(-4)=49++32=81>0 имеет два корня.
х₁=-7+√81\2*2=-7+9\4=2\4=0,5
х₂=-7-√81\2*2=-7-9\4=-16\4=-4
Проверка:
х₁=0,5
√3х²+7х-4=-х
√3*(0,5)²+7*0,5-4=-0,5
√0,75+3,5-4=-0,5
√0,25=-0,5
0,5≠-0,5
х₁=0,5- не является корнем уравнения.
х₂=-4
√3*(-4)²+7*(-4)-4=-(-4)
√48-28-4=4
√16=4
4=4
Ответ : х=-4.