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#### Chipset3600

##### Member

- Feb 14, 2012

- 79

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

- Thread starter Chipset3600
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- Thread starter
- #1

- Feb 14, 2012

- 79

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

- Feb 21, 2013

- 739

Put \(\displaystyle C=(2+\sqrt {2})^x\) Then \(\displaystyle \frac{1}{C}=\frac{1}{(2-\sqrt {2})^x}\)

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

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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