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lizzymichaelis3
@lizzymichaelis3
July 2022
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Решить уравнение: √(3x^2-2x+15)+√(3x^2-2x+8)=7
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Verified answer
Удобно сделать замену: 3x² - 2x + 8 = t ≥ 0
√(t + 7) + √t = 7
√(t + 7) = 7 - √t
t + 7 = 49 - 14√t + t
14√t = 42
√t = 3
t = 9
3x² - 2x + 8 = 9
3x² - 2x - 1 = 0
D=4+4*3=4²
(х)1;2 = (2 +- 4)/6 = (1 +- 2) / 3
х1 = 1
х2 = -1/3
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Answers & Comments
Verified answer
Удобно сделать замену: 3x² - 2x + 8 = t ≥ 0√(t + 7) + √t = 7
√(t + 7) = 7 - √t
t + 7 = 49 - 14√t + t
14√t = 42
√t = 3
t = 9
3x² - 2x + 8 = 9
3x² - 2x - 1 = 0
D=4+4*3=4²
(х)1;2 = (2 +- 4)/6 = (1 +- 2) / 3
х1 = 1
х2 = -1/3