貼圖、程式等,版主可任意修改或刪除,轉貼文章請多用連結,一天 (00:00-23:59) 請只開一個話題,請大家合作,謝謝。05/19/2024 02:52:32 意見庫存 |
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問一個國中數學問題 |
X^2+Y^2=40
X*Y=16 求 X值 y值 |
Record ID: 1714452302 | From: 台灣 |
2*8^0.5
8^0.5 |
Record ID: 1714452302R001 | From: 新加坡 |
两个都是负的也可以 |
Record ID: 1714452302R002 | From: 新加坡 |
X=2×2^0.5 y=4×2^0.5
X=-(2×2^0.5) y=-(4×2^0.5) 或者 上述答案 x y 值互換 所以有4組答案 |
Record ID: 1714452302R003 | From: 台灣 |
有人知道解題過程? |
Record ID: 1714452302R004 | From: 台灣 |
没啥可以特别说的吧
不就是典型的一元二次方程的应用题吗 |
Record ID: 1714452302R005 | From: 新加坡 |
--林獸醫
怎解? |
Record ID: 1714452302R006 | From: 台灣 |
y=16/x
x^2 + 256/x^2 = 40 x^2 - 40x^2 + 256 = 0 (x^2 - 20)^2 -144 = 0 x^2 - 20 = 12 x^2 = 32 |
Record ID: 1714452302R007 | From: 新加坡 |
x^4 - 40x^2 + 256 = 0 |
Record ID: 1714452302R008 | From: 新加坡 |
竟然還要算算術 |
Record ID: 1714452302R009 | From: 台灣 |
X^2+Y^2=40 (1)
X*Y=16 (2) 求 X值 y值 Equation (1) is an equation for a circle of radius sqrt(40) centered at the origin. Equation (2) is a hyperbola. Because xy = 16 that is positive, both x and y should be either positive or negative. This hyperbola would be in the third quadrant or first quadrant. These two curves have four intersection points. They are: X = 4*sqrt(2) Y = 2*sqrt (2) X = 2*sqrt(2) Y = 4*sqrt(2) in the first quadrant; while X = -4*sqrt(2) Y = -2*sqrt (2) X = -2*sqrt(2) Y = -4*sqrt(2) in the third quadrant. |
Record ID: 1714452302R010 | From: 不詳 |
X^2+Y^2=40 是一個以原點為中心的圓 X*Y=16 是一條通過原點的直線 圓和直線的交點... 兩個條件就都滿足了 |
Record ID: 1714452302R011 | From: 台灣 |
X*Y=16 是一條通過原點的直線
Is it true? |
Record ID: 1714452302R012 | From: 不詳 |
Check this link for my solution. |
Record ID: 1714452302R013 | From: 台灣 |
Alternative method
X^2+Y^2=40 (1) X*Y=16 (2) From these two equations, we can do (1) + 2*(2) and (1) - 2*(2) to respectively get X^2+ 2X*Y+Y^2=40 + 2*16 = 72 (3) X^2- 2X*Y+Y^2=40 -2*16 = 8 (4) Then take square root of (3) and (4) to obtain X + Y = (+ or-)6*sqrt(2) X- Y = (+ or -)2*sqrt(2) From these two equations, we find that (+ or-)4*sqrt(2) will be for one symbol and (+ or -)2*sqrt(2) for another. There are four combinations which are shown in R010. |
Record ID: 1714452302R014 | From: 不詳 |
嗯, tt 是對的.
我畫了一下, 那兩條線彎得有夠彎. |
Record ID: 1714452302R015 | From: 台灣 |