{x^2-y=72, {x+y=9. решите систему уровнений

Question

Алгебра: {x^2-y=72, {x+y=9. решите систему уровнений

Leshik1997 · Accepted Answer

Решение
1) 3^(x - 1) - (1/3)^(3 - x) = √((1/9)^(4 - x) + 207
(1/3) * 3^(x)   - (1/27) * (3)^(x) = √(9)^(x) * √( 9⁻⁴) + 207
(1/3) * (3^x)   - (1/27) * (3^x)  - (1/81) * (3^x) =  207
(3^x) * (1/3 - 1/27 - 1/81) = 207
(3^x) * (1/3 - 1/27 - 1/81) = 207
(3^x) * (23/27) = 207
3 ^x = 9*27
3^x = 3^5
x = 5
ответ: х = 5

2) 2^(x^2 +2x-6)-2^(7-2x-x^2)=3,5
2^(x^2 +2x-6) - 2 / [2^(x^2 +2x-6)] = 7/2
z =  2^(x^2 +2x-6) , z > 0
z - 2/z = 7/2
2z² - 7z - 4 = 0
D = 49 + 4*2*4 = 81
z₁ = (7 - 9)/4
z₁ = - 1/2 не удовлетворяет условию: z > 0
z₂ = (7 + 9)/4
z₂ = 4

2^(x^2 +2x-6) = 4
2^(x^2 +2x-6) = 2²
x^2 +2x-6 = 2
x² + 2x - 8 = 0
x₁ = - 4
x₂ = 2
ответ: x₁ = - 4 ; x₂ = 2

MOGZ ответил