5.
121 = 11²
11²ˣ² ⁻²ˣ = 11²⁴
2х² – 2х = 24
х² – х – 12
= 0
D = b² – 4ac
D =
1 – 4 * 1 * (- 12) = 1 + 48 = 49
√D =
√49 = 7
x₁
= (1 + 7)/2 = 8/2 = 4 - наибольший корень
x₂ = (1 - 7)/2 = - 6/2 = - 3
1/3 * 4 + 1 = 4/3 + 1 =
1¹/₃ + 1 = 2 ¹/₃
Ответ: под цифрой
2) 2¹/₃
6.
5⁻ˣ² ⁻ ²ˣ ⁺ ¹² = 5²ˣ
- х² – 2х + 12 = 2х
- х² – 2х + 12 - 2х =
0
х2 + 4х - 12 =
0
D = b² – 4ac
D = 16 – 4
* 1 * (- 12) = 16 + 48 = 64
√D = √64 =
8
x₁ = (- 4 + 8)/2 = 4/2 = 2
x₂ = (- 4 - 8)/2 = -12/2 = - 6
х₁ * х₂ = 2 * ( - 6) = - 12
Ответ: под цифрой 2) [- 14; - 12]
8.
f(x) = g(x)
(¹⁴/₁₀)ˣ² ⁺ ¹ = (¹⁴/₁₀)⁷/₃
х² + 1 = 7/3
3х² + 3 = 7
3x² = 7 - 3
3х² = 4
x² = ⁴/₃
x₁ = √⁴/₃ = ²/√₃
x₂ = - √⁴/₃ = - ²/√₃
х₁ * х₂ = ²/√₃ * ( - ²/√₃) = - ⁴/₃
Ответ: под цифрой 1) – ⁴/₃