# Exponential Equation

#### Chipset3600

##### Member
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
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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