# Expo-equation

#### dhiab

Solve in R:
$$\displaystyle x^{2}\times 2^{\sqrt{2x+1}-1}+2^{x}=2^{\sqrt{2x+1}+1}+x^{2}\times 2^{x-2}$$

Amer

#### Amer

Solve in R:
$$\displaystyle x^{2}\times 2^{\sqrt{2x+1}-1}+2^{x}=2^{\sqrt{2x+1}+1}+x^{2}\times 2^{x-2}$$
$$\displaystyle 2^{\sqrt{2x+1}-1} = 2^{x-2}$$

and find x

$$\displaystyle 2^{\sqrt{2x+1}-1} = 2^{x-2}$$
This only gives the solution $$\displaystyle x = 4$$ (which is correct), but there is also a solution at $$\displaystyle x = 2$$. I think you'll have to replace the $$\displaystyle x^2$$ terms by an expression in the form $$\displaystyle x = 2^y$$ and the compare coefficients to get this solution.