if x^(1/4)+x^(-1/4)=4 , find the values of the following expressions.
(a)(開方x)+(1/開方x)
(b) x+1/x
maths(F.4)
2006-10-23 1:53 am
回答 (2)
2006-10-23 1:58 am
✔ 最佳答案
x^(1/4)+x^(-1/4)=4(a) Taking square for both sides, we have
[x^(1/4)+x^(-1/4)]^2=16
(開方x)+2+ (1/開方x) = 16
(開方x)+ (1/開方x) = 14
(b) Taking square for both sides of the result of (a) above, we have
[(開方x)+ (1/開方x)]^2 = 196
x +2 + (1/x) = 196
x + (1/x) = 194
參考: I, me and myself
2006-10-23 2:00 am
sqrt = 開方
(a)
x^(1/4) + x^(-1/4) =4
[x^(1/4) + x^(-1/4)]^2 =4^2
sqrt(x) + 2 + 1/sqrt(x) = 16
sqrt(x) + 1/sqrt(x) = 14
(b)
sqrt(x) + 1/sqrt(x) = 14
[sqrt(x) + 1/sqrt(x)]^2 = 14^2
x + 2 + 1/x = 196
x + 1/x = 194
(a)
x^(1/4) + x^(-1/4) =4
[x^(1/4) + x^(-1/4)]^2 =4^2
sqrt(x) + 2 + 1/sqrt(x) = 16
sqrt(x) + 1/sqrt(x) = 14
(b)
sqrt(x) + 1/sqrt(x) = 14
[sqrt(x) + 1/sqrt(x)]^2 = 14^2
x + 2 + 1/x = 196
x + 1/x = 194
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