Consider the equation (*): x^2-4x+m=√(x^2-4x+m) +42, where m is a constant.
a) Find the value(s) of √(x^2-4x+m).
b) If the roots of (*) are intergers, using the result (a), give two possible sets of the roots and the corresponding value of m.
唔識做功課60
2015-04-10 8:32 am
回答 (2)
2015-04-10 8:51 am
✔ 最佳答案
Please read:圖片參考：https://s.yimg.com/rk/HA00430218/o/870558062.png
2015-04-10 00:52:29 補充：
Here I gave you 4 possible sets but you only need 2.
2015-04-10 00:53:52 補充：
Typo:
In the last line, it should be "2 (repeated)" rather than "0 (repeated)".
2015-04-10 03:05:42 補充：
﹝｡◕‿◕｡◕‿◠｡﹞
2015-04-10 10:39 am
There may be another method. = )
For b,
√(x² - 4x + m - 49) = 7
x² - 4x + m - 49 = 0
sum of roots = α+β = 4
Let α = 1 and β = 3
m - 49 = αβ
m = 3 + 49 = 52
Let α = 2 and β = 2
m - 49 = αβ
m = 4 + 49 = 53
2015-04-10 02:49:46 補充：
* √(x² - 4x + m) = 7
For b,
√(x² - 4x + m - 49) = 7
x² - 4x + m - 49 = 0
sum of roots = α+β = 4
Let α = 1 and β = 3
m - 49 = αβ
m = 3 + 49 = 52
Let α = 2 and β = 2
m - 49 = αβ
m = 4 + 49 = 53
2015-04-10 02:49:46 補充：
* √(x² - 4x + m) = 7
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