推 sugar317 :感謝解惑!! 05/09 11:23
※ 引述《sugar317 (shadow)》之銘言：
: x^2-y^2=24
: 2xy=10
: 要怎換比較好解呢
: 麻煩一下
x^2 - y^2 = 24 -------(1)
2xy = 10 -------(2)
5
(2) => y = --- 代入(1)得
x
25
x^2 - ----- = 24
x^2
x^4 - 25 = (24)(x^2)
=> x^4 - (24)(x^2) - 25 = 0
=> (x^2 + 1)(x^2 - 25) = 0
∵ x^2 + 1 ≠ 0
∴ x^2 - 25 = 0 => (x + 5)(x - 5) = 0
∴ x = -5或5
代入(2)得 y = -1或1
∴ (x,y) = (-5,-1) 或 (5,1)
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