Х2 – 15х + 56 = 0 Решение. х2 – 7х – 8х + 56 = 0, - вопрос №1689537121556027856027856 от oDESo 01.11.2020 13:44

Question

Алгебра: Х2 – 15х + 56 = 0 Решение. х2 – 7х – 8х + 56 = 0, (х2 – 7х) – (8х – 56) =0, х(х – 7) – 8(х – 7) = 0, (х – 7)(х – 8) = 0, х=7, х решите. ​

oDESo · Answer

1) log₀₎₂²(x/25) = log₀₎₂(x/25)*log₀₎₂(x/25) =
= ( log₀₎₂x - log₀₎₂25)*( log₀₎₂x - log₀₎₂25)= (log₀₎₂x +2)* (log₀₎₂x +2)=
= (log₀₎₂x +2)²= log₀₎₂²x +4log₀₎₂x +4
2)log₀₎₂²(x/5) = log₀₎₂(x/5)*log₀₎₂(x/5) = (log₀₎₂x - log₀₎₂5)*(log₀₎₂x - log₀₎₂5)=
=(log₀₎₂x +1)*(log₀₎₂x +1)= (log₀₎₂x +1)² = log₀₎₂²x + 2log₀₎₂x +1
3) Само уравнение:
log₀₎₂²x +4log₀₎₂x +4 +log₀₎₂²x + 2log₀₎₂x +1 = 1 (ОДЗ: x > 0)
log₀₎₂x = t
t² +4t +4 +t² +2t = 0
2t² +6t +4 = 0
t² +3t +2 = 0
По т. Виета
а) t = -2, ⇒ log₀₎₂x = -2, x = 0,2⁻² = 25
б) t = -1, ⇒ log₀₎₂x = -1, ⇒ x = 0,2⁻¹ = 5
ответ: 125

Х2 – 15х + 56 = 0 Решение. х2 – 7х – 8х + 56 = 0, (х2 – 7х) – (8х – 56) =0, х(х – 7) – 8(х – 7) = 0, (х – 7)(х – 8) = 0, х=7, х решите. ​

Х2 – 15х + 56 = 0 Решение. х2 – 7х – 8х + 56 = 0, (х2 – 7х) – (8х – 56) =0, х(х – 7) – 8(х – 7) = 0, (х – 7)(х – 8) = 0, х=7, х решите.