數 學 問 題

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3x + 2y = 9xy + 6y² - 9x² = 2

{3x+2y=2 ...(1)
{9xy+6y²-9x²=2 ...(2)

從(1) 得知 y = (2-3x)/2, 代入 (2)

9x[(2-3x)/2] + 6[(2-3x)/2]² - 9x² = 2

9x(2-3x)/2 + 6(2-3x)²/4 - 9x² = 2

全式乘4

18x(2-3x) + 6(2-3x)² - 36x² = 8

36x - 54x² + 6(4-12x+9x²) - 36x² = 8

36x - 54x² + 24 - 72x + 54x² - 36x² = 8

36x + 24 - 72x - 36x² = 8

- 36x² - 36x + 16 = 0

36x² + 36x - 16 = 0

9x² + 9x - 4 = 0

(3x - 1)(3x + 4) = 0

x = 1/3 or x = -4/3

For x = 1/3, y = (2-3x)/2 = y = (2-1)/2 = 1/2

For x = -4/3, y = (2-3x)/2 = y = (2+4)/2 = 3

(x, y) = (1/3, 1/2) or (-4/3, 3)

3x+2y=2

>>>y=1-3x/2


9x(1-3x/2)+6(1-3x/2)^2-9x^2=2

>>>9x(4-6x)+6(2-3x)^2-36x^2=8

>>>36x-54x^2+6(9x^2-12x+4)-36x^2-8=0

>>>36x-54x^2+54x^2-72x+24-36x^2-8=0

>>>-36x^2-36x+16=0

2013-10-12 21:12:50 補充：
>>>9x^2+9x-4=0

>>>(3x-1)(3x+4)=0

>>>x=1/3 or -4/3

>>>y=1-3x/2=1/2 or 3

∴(x,y)=(1/3,1/2) or (-4/3,3)