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\( \Sigma ( x + 2 ) ^ { 2 } = 480 \)

Ask by Gordon Washington. in India
Feb 28,2025

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The sum of (x + 2) squared equals 480. To solve for x, you need to know the range of summation or if x is a constant. Please provide more information about the summation index or the values of x to find the solution.

Solución

I’d be happy to help, but I need a bit more clarification about the expression you provided. You wrote   Σ (x + 2)² = 480 Here are a few questions that can help me give you the correct answer: 1. What is the index of summation? For example, is the sum written as   Σ₍ᵢ₌₁₎ⁿ (x₍ᵢ₎ + 2)² = 480 or are we summing over some specific range or set of values for x? 2. Is x a constant (with the same value in every term) or is it an index (with different values for each term)? 3. If x is the same in every term, does the sigma notation indicate that there are a fixed number of terms (say n terms) so that the sum is n·(x + 2)² = 480? If you could clarify the intended meaning (for example, the range of summation or the role of x), I’ll be able to assist you in solving the problem.

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Beyond the Answer

To solve \( \Sigma ( x + 2 ) ^ { 2 } = 480 \), let's expand \( (x + 2)^2 \) first. This gives us \( x^2 + 4x + 4 \). Now, summing this expression over a certain number of terms means you are summing up the quadratic from a specific starting point to \( n \). Assuming you're summing from \( x = 1 \) to \( n \), you could use the formula for the sum of squares and the sum of integers. But, since you've set this equal to 480, we actually need to find values of \( x \) such that the cumulative total equals 480! You can also rearrange it into a more workable form: 1. Determine how many terms are involved \( n \). 2. Solve for \( n \) using the area or summation formulas. This brings you closer to finding \( x \) that meets this equation! Let’s crunch some numbers!

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