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VeryIntelligent
@VeryIntelligent
July 2022
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Как решить уравнение: 4/(3^sqrt (x)+(3^sqrt (x)+3)/5=2 ?
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Удачник66
Verified answer
Замена корень куб.(x) + 2 = y, тогда корень куб(x) + 3 = y + 1
4/y + (y+1)/5 = 2
Умножаем все на y и на 5
4*5 + y(y+1) - 2*5y = 0
20 + y^2 + y - 10y = y^2 - 9y + 20 = 0
(y - 4)(y - 5) = 0
1) y = корень куб(x) + 2 = 4
корень куб(x) = 4 - 2 = 2
x1 = 2^3 = 8
2) y = корень куб(x) + 2 = 5
корень куб(x) = 5 - 2 = 3
x2 = 3^3 = 27
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Answers & Comments
Verified answer
Замена корень куб.(x) + 2 = y, тогда корень куб(x) + 3 = y + 14/y + (y+1)/5 = 2
Умножаем все на y и на 5
4*5 + y(y+1) - 2*5y = 0
20 + y^2 + y - 10y = y^2 - 9y + 20 = 0
(y - 4)(y - 5) = 0
1) y = корень куб(x) + 2 = 4
корень куб(x) = 4 - 2 = 2
x1 = 2^3 = 8
2) y = корень куб(x) + 2 = 5
корень куб(x) = 5 - 2 = 3
x2 = 3^3 = 27