1. Stated problem: Solve the equation $$\frac{4^{2}+1+4^{2}}{2^{2}+1-2^{2}\cdot 2}=25$$. 2. Simplify powers and expressions in numerator and denominator: - Numerator: $$4^2=16$$, thus $$16+1+16=33$$. - Denominator: $$2^2=4$$, calculate $$4+1-4\cdot 2=4+1-8=-3$$. 3. Substitute simplified values into the fraction: $$\frac{33}{-3} = -11$$. 4. Check if the equation $$-11=25$$ holds. It does not. 5. Conclusion: The equation as stated $$\frac{4^{2}+1+4^{2}}{2^{2}+1-2^{2}\cdot 2}=25$$ is false; the left side equals $$-11$$, not $$25$$. Final answer: $$\boxed{-11 \neq 25}$$.