在附加數學中,我們知道√(x²) = | x |
但請問,(√x )² = ?
答案會不會也是| x | ? 為什麼?
將一個未知數開方再二次方...........
2007-02-22 10:56 pm
回答 (5)
2007-02-23 4:35 am
2次方和開方根抵消√x²
= x
但(√x)²即是將x開方再2次方..即是x
所以我想應該也是x吧
e.g:√5 =2.236067977
再2次方..不也是5嗎?!
= x
但(√x)²即是將x開方再2次方..即是x
所以我想應該也是x吧
e.g:√5 =2.236067977
再2次方..不也是5嗎?!
參考: 冇
2007-02-23 1:45 am
No, take x = -1, you get
√-1 = i or -i, however (√x )² = -1
which is not equal to | -1| = 1
Note that in general √(x²) = | x | is true for all real x, but (√x )² = x is true for all positive real x, since any positive number under square rot sign must be positive (no absolute sign is needed.
√-1 = i or -i, however (√x )² = -1
which is not equal to | -1| = 1
Note that in general √(x²) = | x | is true for all real x, but (√x )² = x is true for all positive real x, since any positive number under square rot sign must be positive (no absolute sign is needed.
2007-02-22 11:46 pm
答案是X
因爲(√x )² 中已經保證x大於或等於0，二次方後可直接等於x,
注意，這是從實數角度考慮。虛數角度不用了，別鑽牛角尖。
因爲(√x )² 中已經保證x大於或等於0，二次方後可直接等於x,
注意，這是從實數角度考慮。虛數角度不用了，別鑽牛角尖。
2007-02-22 11:04 pm
未必會
在真數列 (real number), 這個是真的, 例如4, 開方後再sqrt之後亦是等於4. 即是等於正4.
不過在虛數列中 (complex number), 如果 -9, 開方後變成 3i, i^2 = -1, 當你sqrt. 左就會變成 3^2x(-1) = -9
所以(rt. x) ^2 之後的答案, 只可說成 x, 而不可以 |x|.
在真數列 (real number), 這個是真的, 例如4, 開方後再sqrt之後亦是等於4. 即是等於正4.
不過在虛數列中 (complex number), 如果 -9, 開方後變成 3i, i^2 = -1, 當你sqrt. 左就會變成 3^2x(-1) = -9
所以(rt. x) ^2 之後的答案, 只可說成 x, 而不可以 |x|.
參考: nil
收錄日期: 2021-04-13 14:17:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070222000051KK02540