標題:
中二數學~~ (40分 @5)
發問:
利用公式法求出下列各一元二次方程的解(x), 若解是無理數, 請用根號表示或準確至三位有效數字 1. 13x2 - 7x + 9 = 8 2. 100x2 + 8x = 14 3. 84x2 = 56 - 96x 4. 56 + 81x - 57x2 = 0 5. 99x2 - 77x - 66 = 22 6. 13x2 + 28x + 1328 = 2656 7. 10x2 + 35x = 8 8. 1215x2 + 1020x - 1118 = 0 更新: csw97 is the best~!
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利用公式法求出下列各一元二次方程的解(x), 若解是有理數, 請用根號表示或準確至三位有效數字 1. 13x2 - 7x + 9 = 8 13x2 - 7x + 1 = 0 判別式為 B2-4AC (-7)2 – 4(13)(1) = -3 所以沒有實根 2. 100x2 + 8x = 14 100x2 + 8x – 14 = 0 x = {-8±√[(8)2 – 4(100)(-14)]}/[2(100)] x = 0.336 或 x = -0.416 3. 84x2 = 56 - 96x 84x2 + 96x - 56 = 0 x = {-96±√[(96)2 – 4(84)(-56)]}/[2(84)] x = 0.425 或 x = -1.57 4. 56 + 81x - 57x2 = 0 x = {-81±√[(81)2 – 4(-57)( 56)]}/[2(-57)] x = -0.509 或 x = 1.93 5. 99x2 - 77x - 66 = 22 99x2 - 77x - 88 = 0 9x2 - 7x - 8 = 0 x = {7±√[(-7)2 – 4(9)(-8)]}/[2(9)] x = 1.41 或 x = -0.631 6. 13x2 + 28x + 1328 = 2656 13x2 + 28x – 1328 = 0 x = {-28±√[(28)2 – 4(13)(-1328)]}/[2(13)] x = 9.09 或 x = -11.2 7. 10x2 + 35x = 8 10x2 + 35x – 8 = 0 x = {-35±√[(35)2 – 4(10)(- 8)]}/[2(10)] x = 0.215 或 x = -3.72 8. 1215x2 + 1020x - 1118 = 0 1215x2 + 1020x - 1118 = 0 x = {-1020±√[(1020)2 – 4(1215)(-1118)]}/[2(1215)] x = 0.627 或 x = -1.47
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