[Dal]

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!

[the bear]

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

[AlphaNumeric]

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It works because of the nice expression. More generally The Bear's method is best.

[Dal]

thanks for the help!

[carol05]

let e^x = W

W + 1/W = 2

W² + 1 = 2W

W² - 2W + 1 = 0

(W - 1)² = 0

W = 1

e^x = 1

x=0
You don't need to use logs. Any number, except 0, to the power of 0 equals 1

[AlphaNumeric]

Originally Posted by carol05

Any number to the power of 0 equals 1

What about 0

[carol05]

Originally Posted by AlphaNumeric

What about 0

Thanks for the correction.