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Exponential Equation

Chipset3600

Member
Feb 14, 2012
79
Hi, i'm having problems to solve this equation, pls help me:

\(\displaystyle \left( 2+\sqrt {2}\right) ^{x}+\left( 2-\sqrt {2}\right) ^{x}=4\)
 

Petrus

Well-known member
Feb 21, 2013
739
Hi, i'm having problems to solve this equation, pls help me:

\(\displaystyle \left( 2+\sqrt {2}\right) ^{x}+\left( 2-\sqrt {2}\right) ^{x}=4\)
Put \(\displaystyle C=(2+\sqrt {2})^x\) Then \(\displaystyle \frac{1}{C}=\frac{1}{(2-\sqrt {2})^x}\)
NOW MY QUESTION IS, HOW DID I GET THIS?

Hint:
\(\displaystyle (2+\sqrt {2})^x (2-\sqrt {2})^x\)


Regards,
\(\displaystyle |\pi\rangle\)
 
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