Maths
回答 (3)
2013-04-25 9:01 pm
✔ 最佳答案
x(x^2-3)>0Case 1
x>0 and X^2-3>0 => x<0 and -(3^0.5)<X<3^0.5 =>-(3^0.5)<x<0
Case 2
X>0 and X^2-3>0
=> X>0 and X^2>3
=>X>0 and X<-3^0.5 (Rejected because impossible) or X>0 and X>3^0.5
=>X>3^0.5
Ans: -3^0.5< X < 0 or X>3^0.5
2013-04-25 11:13 pm
x (x² - 3) > 0
(x + √3) x (x - √3) > 0
Case I : x < -√3
(x + √3) x (x - √3) < 0
Case II : -√3 < x < 0
(x + √3) x (x - √3) > 0
Case III : 0 < x < √3
(x + √3) x (x - √3) < 0
Case IV : x > √3
(x + √3) x (x - √3) > 0
Hence, range of x :
-√3 < x < 0 and x > √3 ... (ans)
(x + √3) x (x - √3) > 0
Case I : x < -√3
(x + √3) x (x - √3) < 0
Case II : -√3 < x < 0
(x + √3) x (x - √3) > 0
Case III : 0 < x < √3
(x + √3) x (x - √3) < 0
Case IV : x > √3
(x + √3) x (x - √3) > 0
Hence, range of x :
-√3 < x < 0 and x > √3 ... (ans)
2013-04-25 6:01 pm
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