續二次方程(11-14題)

11.
設 u = √(x + 6)

1 + √(x + 6) = 2/√(x + 6)
1 + u = 2/u
u^2 + u - 2 = 0
(u - 1)(u + 2) = 0
u = 1 或 u = -2
√(x + 6) = 1 或 √(x + 6) = -2(不合)
x + 6 = 1
x = -5


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12.
設 u = 1/√(x - 3)

[2/(x - 3)] + 3 = 7/√(x - 3)
2u^2 + 3 = 7u
2u^2 - 7u + 3 = 0
(2u - 1)(u - 3) = 0
u = 1/2 或 u = 3
1/√(x - 3) = 1/2 或 1/√(x - 3) =3
√(x - 3) = 2 或 √(x - 3) = 1/3
x - 3 = 4 或 x - 3 = 1/9
x = 7 或 x = -28/9


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13.
設 u = 2^x

2^2x - 3[2^(x+2)] +32 = 0
(2^x)^2 - 3[(2^2)*(2^x)] + 32 = 0
(2^x)^2 - 12(2^x) + 32 = 0
u^2 - 12u + 32 = 0
(u - 4)(u - 8) = 0
u = 4 或 u = 8
2^x = 2^2 或 2^x = 2^3
x = 2 或 x = 3


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14.
設 u = 3^x

9^x + 2(3^x) - 3 =0
(3^x)^2 + 2(3^x) - 3 = 0
u^2 + 2u - 3 = 0
(u - 1)(u + 3) = 0
u = 1 或 u = -3
3^x = 3^0 或 3^x = -3(不合)
x = 0