решите систему уравнений а)15x^2-2xy=5 и 2x-y=3. Created by pryklychenia. algebra-ru

решите систему уравнений а)15x^2-2xy=5 и 2x-y=3...

pryklychenia @pryklychenia

July 2022 1 11 Report

решите систему уравнений а)15x^2-2xy=5 и 2x-y=3

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Verified answer

15x² - 2xy = 5
2x - y = 3

15x² - 2xy = 5
y = 2x - 3

15x² - 2x(2x - 3) - 5 = 0
y = 2x - 3

15x² - 4x² + 6x - 5 = 0
y = 2x - 3

11x² + 6x - 5 = 0
D = 36 + 5•11•4 = 256 = 16²
x1 = (-6 + 16)/22 = 10/22 = 5/11
x2 = (-6 - 16)/2 = -22/22 = -1

x = 5/11
y = 2•5/11 - 3

x = -1
y = -2 - 3

x = 5/11
y = -23/11

x = -1
y = -5
Ответ: (5/11; -23/11); (-1; -5).

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