Amaths 數[[ quadratic equations]]

1) y^2/3-13y^1/3+36=0

設 x = y^1/3, 則
x^2 - 13x + 36 = 0
(x - 4)(x - 9) = 0
x = 4 或 x = 9

當x = 4,
y^1/3 = 4
y = 64

當x = 9,
y^1/3 = 9
y = 729

所以 y = 64 或 y = 729

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2) 2y-9y^1/2+4=0

設 x = y^1/2, 則
2x^2 - 9x + 4 = 0
(2x - 1)(x - 4) = 0
x = 1/2 或 x = 4

當x = 1/2,
y^1/2 = 1/2
y = 1/4

當x = 4,
y^1/2 = 4
y = 16

所以 y = 1/4 或 y = 16

2007-01-01 12:07:11 補充：
驗算:1.(64)^2/3 - 13(64)^1/3 36 = 16 - 52 36 = 0(729)^2/3 - 13(729)^1/3 36 = 81 - 117 36 = 02.2(1/4) - 9(1/4)^1/2 4 = 0.5 - 4.5 4 = 02(16) - 9(16)^1/2 4 = 32 - 36 4 = 0

1) y^2/3-13y^1/3+36=0

Let x by y^(1/3), then the equation becomes:

x^2-13x+36=0
(x - 9)(x - 4) = 0
x = 9 or x = 4
y^(1/3) = 9 or y^(1/3) = 4
y = 9^3 = 729 or y = 4^3 = 64

2) 2y-9y^1/2+4=0

Let x by y^(1/2), then the equation becomes:

2x^2-9x+4=0
(2x - 1)(x - 4) = 0
x = 1/2 or x = 4
y = (1/2)^2 = 1/4 or y = 4^2 = 16

關鍵係 Let something so that 條 equation 可以變成 quadratic equation.