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Koshka6996
@Koshka6996
July 2022
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Розв’язати систему рівнянь з двома змінними х²-ху+у=16,3у-х=14
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Verified answer
Х² - ху + у = 16
3у - х = 14
х² - ху + у = 16
х = 3у - 14
(3у - 14)² - у(3у - 14) + у - 16 = 0
х = 3у - 14
9у² - 84у + 196 - 3у² + 14у + у - 16 = 0
х = 3у - 14
6у² - 69у + 180 = 0
х = 3у - 14
2у² - 23у + 60 = 0
D = 23² - 60•2•4 = 529 - 480 = 49 = 7²
y1 = (23 + 7)/4 = 30/4 = 7,5.
y2 = (23 - 7)/4 = 16/4 = 4.
y = 7,5
x = 7,5•3 - 14
y = 4
y = 3•4 - 14
y = 7,5
x = 8,5
y = 4
x = -2
Ответ: (-2; 4), (8,5; 7,5).
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Answers & Comments
Verified answer
Х² - ху + у = 163у - х = 14
х² - ху + у = 16
х = 3у - 14
(3у - 14)² - у(3у - 14) + у - 16 = 0
х = 3у - 14
9у² - 84у + 196 - 3у² + 14у + у - 16 = 0
х = 3у - 14
6у² - 69у + 180 = 0
х = 3у - 14
2у² - 23у + 60 = 0
D = 23² - 60•2•4 = 529 - 480 = 49 = 7²
y1 = (23 + 7)/4 = 30/4 = 7,5.
y2 = (23 - 7)/4 = 16/4 = 4.
y = 7,5
x = 7,5•3 - 14
y = 4
y = 3•4 - 14
y = 7,5
x = 8,5
y = 4
x = -2
Ответ: (-2; 4), (8,5; 7,5).