MHB Solve Exponential Equation: 2+√2^x + 2-√2^x =4

[Chipset3600]

Hi, I'm having problems to solve this equation, pls help me:

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

 

[Petrus]

Hi, I'm having problems to solve this equation, pls help me:

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

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

Hint:

Spoiler

$$(2+\sqrt {2})^x (2-\sqrt {2})^x$$

Regards,
$$|\pi\rangle$$