Three numbers have a sum of squares of 138 and pairwise products summing to 131. Find their sum:___________?
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Answer: A. 20
Explanation
The algebraic identity for the square of a three term sum expands into individual squares and pairwise products. Substituting the given sum of squares and pairwise product sums into the expanded identity gives one thirty eight plus two times one thirty one. Evaluating this numerical expression yields four hundred, and taking the square root gives the final sum of twenty. Algebraic expansion formulas provide shortcuts for evaluating complex polynomial expressions without direct multiplication. The square of a sum identity connects the sum of individual variables directly to their squared values and cross products. Taking the square root of a positive squared sum yields both positive and negative valid mathematical roots.
Thirty is incorrect because it represents an arithmetic error during the final square root evaluation step. Forty would incorrectly result from failing to take the square root of the final expanded expression value. None of these is incorrect because the first option provides the mathematically accurate answer to the problem.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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