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數學知識交流---二元方程
發問:
已知 7 > x > -10， 解方程 x^2 - y^2 = 17.52 yx^2 + yx^2 = 836.294
最佳解答:
為何 y3+17.52y-418.147=0 會變成 (10x-67)(0.1x2+0.67x+6.241)=0？ 最後答案也錯。 2011-09-21 19:22:55 補充： 解： x2 - y2 = 17.52 ---------(1) 2x2y = 836.294 ---------(2) 由(1)，得： x2 = 17.52 + y2 ---------(3) 把(3)代入(2)，得： 2y (17.52 + y2) = 836.294 (y2 + 17.52) y = 418.147 y3 + 17.52y - 418.147 = 0 (y - 6.7)(y2 + 6.7y + 62.41) = 0 所以y = 6.7 或 y2 + 6.7y + 62.41 = 0 (Δ
其他解答:
7>x>-10------(1) x2-y2=17.52------(2) x2y+x2y=836.294------(3) From (3), 2x2y=836.294 x2y=418.147------(4) From (2). x2=17.52+y2------(5) Sub (5) into (4) (17.52+y2)y=418.147 y3+17.52y-418.147=0 (10x-67)(0.1x2+0.67x+6.241)=0 x=67/10 or [-0.67±√(-2.0475)]/2 {rej. [From (1),(it involve complex number)]} From (5), y2=x2-17.52 y=±√(x2-17.52)------(6) Sub x=67/10 into (6) y=±√(4489/100-17.52) y=±√27.37 Sub y=±27.37 into (5) x2=17.52+27.37 x=±√44.89 x=±6.7 So, x=±6.7, y=±√27.37|||||'yx^2 + yx^2 = 836.294'?? is it wrong? 2011-09-07 19:28:01 補充： two 'yx^2' ??!! 2011-09-07 19:48:21 補充： so u mean 2yx^2=836.294, right? 2011-09-07 20:23:52 補充： 7>x>-10------(1) x2-y2=17.52------(2) x2y+x2y=836.294------(3) From (3), 2x2y=836.294 x2y=418.147------(4) From (2). x2=17.52+y2------(5) Sub (5) into (4) (17.52+y2)y=418.147 y3+17.52y-418.147=0 (10x-67)(0.1x2+0.67x+6.241)=0 x=67/10 or [-0.67±√(-2.0475)]/2 {rej. [From (1),(it involve complex number)]} From (5), y2=x2-17.52 y=±√(x2-17.52)------(6) Sub x=67/10 into (6) y=±√(4489/100-17.52) y=±√27.37 Sub y=±27.37 into (5) x2=17.52+27.37 x=±√44.89 x=±6.7 So, x=±6.7, y=±√27.37 2011-09-15 21:12:17 補充： To kon******: U COPY MY ANSWER??!!!!!|||||No , it isn't wrong . 2011-09-07 19:51:24 補充： You're right .
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