The discussion centers on solving the exponential equation $$\left( 2+\sqrt {2}\right) ^{x}+\left( 2-\sqrt {2}\right) ^{x}=4$$. A user introduces the substitution $$C=(2+\sqrt {2})^x$$ and seeks clarification on how to derive the relationship $$\frac{1}{C}=\frac{1}{(2-\sqrt {2})^x}$$. This transformation is essential for simplifying the equation and finding the value of x.
PREREQUISITESStudents, educators, and anyone interested in advanced algebra, particularly those looking to enhance their skills in solving exponential equations.
Put $$C=(2+\sqrt {2})^x$$ Then $$\frac{1}{C}=\frac{1}{(2-\sqrt {2})^x}$$Chipset3600 said:Hi, I'm having problems to solve this equation, pls help me:
$$\left( 2+\sqrt {2}\right) ^{x}+\left( 2-\sqrt {2}\right) ^{x}=4$$