F.4 maths question

[匿名]

2009-10-03 2:16 am

It's given that g(x+1/x)=x²+1/x²

Find the value of x such that g(x)=-1.

Remark:My teacher gives me the answer as follow:
g(x+1/x)=x²+1/x²
g(x+1/x)=(x+1/x)²-2
g(x)=x²-2
g(x)=-1
x²-2=-1
x²=1
x=+/-1
I don't know why g(x+1/x) suddenly become g(x). Can u explain it to me.
And can u have and give another method to answer this question.

Thanks you!

回答 (1)

用戶2053

2009-10-03 4:21 am

✔ 最佳答案

This method may clearly :
g(x+1/x)=x+1/x
g(x+1/x)=(x+1/x)-2
g(Y) = Y - 2
((x+1/x) is a variable, just a name ,indeeded by Y)
When Y = x :
g(x) = x - 2
- 1 = x - 2
x = +/- 1

2009-10-02 21:12:40 補充：
This method may clearly :

g(x+1/x)=x^2+1/x^2

g(x+1/x)^2=(x+1/x)^2 - 2

g(Y) = Y^2 - 2

((x+1/x) is a variable, just a name ,indeeded by Y)

When Y = x :

g(x) = x^2 - 2

- 1 = x^2 - 2

x = +/- 1

2009-10-02 21:14:05 補充：
The second line correct to

g(x+1/x) = (x+1/x)^2 - 2

sorry!

2009-10-02 21:16:41 補充：
This method may clearly :

g(x+1/x)=x^2 + 1/x^2

g(x+1/x)=(x+1/x)^2 - 2

g(Y) = Y^2 - 2

((x+1/x) is a variable, just a name ,indeeded by Y)

When Y = x :

g(x) = x^2 - 2

- 1 = x^2 - 2

x = +/- 1

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