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The numerical value of \((49x^2 - 56x - 2005)^{10}\) when \( x = \frac{4 + \sqrt{2025}}{7} \) is \( 1,048,576 \).

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Here are 5 related questions to explore further:
1. How is the square root of a number like 2025 calculated?
2. Why does substituting values into quadratic expressions yield specific results?
3. What role does exponentiation play in amplifying the results of an expression?
4. How do different values of \(x\) affect the result of quadratic equations?
5. Can this method be applied to solve higher-order polynomials?

**Tip:** Always simplify radical expressions, like \(\sqrt{2025}\), to make further calculations easier.

When x = (4 + √2025)/7, what is the numerical value of (49x^2 - 56x - 2005)^10?

Calculate the numerical value of (49x^2 - 56x - 2005)^10 when x = (4 + √2025) / 7. Learn how to simplify the expression by solving for x and applying exponentiation techniques. This problem involves algebraic manipulation and is suitable for high school students in Grades 10-12.

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