x=1/4 or x=9/4
有冇錯？
但係書個答案得一個[9/4]既？
1/4我試左,岩
discriminant >0,two unequal real roots
係咪我太介意書個answer呢？
定係我計錯？
(2√x+1)(2√x-3)=0 有冇錯？
4x-4√x-3=0
2007-08-25 9:31 pm
回答 (4)
2007-08-25 9:40 pm
✔ 最佳答案
Let y = √x, then4y^2 - 4y - 3 = 0
( 2y - 3 )( 2y + 1 ) = 0
y = 3 / 2 or y = - 1 / 2
√x = 3 / 2 or √x = - 1 / 2 ( rejected, as sqr cannot be negative )
Then
x = 9 / 4
2007-08-25 13:45:29 補充：
Checking, when x = 1 / 4, L.H.S. = 4 ( 1 / 4 ) - 4 √( 1 / 4 ) - 3 = 1 - 2 - 3 = -4 不等於R.H.S. 所以x = 1 / 4 不成立
2007-08-25 13:58:19 補充：
再補充一下為何要捨去√x = - 1 / 2 , 因為實數的偶次方必為正數或0，所以偶次方根的被開方數如同平方根必須為非負數。
參考: My Maths Knowledge
2007-08-25 9:46 pm
Let y = √x
4y^2 - 4y - 3 = 0
( 2y - 3 )( 2y + 1 ) = 0
y = 3 / 2 or y = - 1 / 2
√x = 3 / 2 or √x = - 1 / 2 ( rejected, squareroot cannot be negative )
So
x = 9 / 4
4y^2 - 4y - 3 = 0
( 2y - 3 )( 2y + 1 ) = 0
y = 3 / 2 or y = - 1 / 2
√x = 3 / 2 or √x = - 1 / 2 ( rejected, squareroot cannot be negative )
So
x = 9 / 4
參考: me
2007-08-25 9:42 pm
答案係9/4.
If the answer is 1/4:
=4x(1/4) - 4√(1/4) - 3
=1 - 4(1/2) - 3
=1 - 2 - 3
= - 4
which is not equal to 0
If the answer is 1/4:
=4x(1/4) - 4√(1/4) - 3
=1 - 4(1/2) - 3
=1 - 2 - 3
= - 4
which is not equal to 0
2007-08-25 9:42 pm
對..只有9/4.
因 √x= -1/2 在實數範圍是不存在的.
因在實數範圍內某何數的平方根都不會是負數.
故這個答案會捨去.
因 √x= -1/2 在實數範圍是不存在的.
因在實數範圍內某何數的平方根都不會是負數.
故這個答案會捨去.
收錄日期: 2021-04-13 13:58:34
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070825000051KK02011