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Old 11-11-2005: 11th November 2005 09:07 #1 
Dal Dal is offline
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Hey!
Can anyone help with the following question?
Ex 3c Q2e:
e^x + e^-x = 2

Is there any way to show that x=0?

thanks!
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Old 11-11-2005: 11th November 2005 09:12 #2 
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Originally Posted by Amirahkassim
Hey!
Can anyone help with the following question?
Ex 3c Q2e:
e^x + e^-x = 2

Is there any way to show that x=0?

thanks!

let e^x = W

W + 1/W = 2

W² + 1 = 2W

W² - 2W + 1 = 0

(W - 1)² = 0

W = 1

e^x = 1

ln( e^x) = ln1

xlne = 0

x*1 = 0

x = 0/1

x = 0

i thank you
Old 11-11-2005: 11th November 2005 09:37 #3 
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[Mimetex cannot convert this formula]
[Mimetex cannot convert this formula]
[Mimetex cannot convert this formula]
[Mimetex cannot convert this formula]
[Mimetex cannot convert this formula]

It works because of the nice expression. More generally The Bear's method is best.
Old 11-11-2005: 11th November 2005 13:20 #4 
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thanks for the help!
Old 11-11-2005: 11th November 2005 14:20 #5 
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let ex = W

W + 1/W = 2

W² + 1 = 2W

W² - 2W + 1 = 0

(W - 1)² = 0

W = 1

ex = 1

x=0
You don't need to use logs. Any number, except 0, to the power of 0 equals 1
Old 11-11-2005: 11th November 2005 14:58 #6 
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Originally Posted by carol05
Any number to the power of 0 equals 1
What about 0
Old 11-11-2005: 11th November 2005 15:02 #7 
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Originally Posted by AlphaNumeric
What about 0

Thanks for the correction.
 
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