The mean of a non-zero number and its square equals 5 times the number. Find the number__________?
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Answer: A. 9
Explanation
Expressing the mean of a number and its square creates the algebraic expression x plus x squared over two. Equating this mean expression to five times the number forms a solvable polynomial equation. Dividing the non-zero variable x from both sides simplifies the equation to yield nine. Polynomial equations can often be simplified by factoring out common variable terms safely. Non-zero constraints ensure that division by the variable does not result in undefined mathematical operations. The arithmetic mean of any two quantities is found by adding them and dividing by two.
Algebraic modeling helps solve abstract numerical puzzles used in mathematical competitions and aptitude tests. Quadratic relationships appear frequently in physics when modeling motion and area optimization. Understanding polynomial simplification is fundamental for advanced algebra and calculus coursework. Option B suggests seventeen which does not satisfy the balanced mean equation condition. Option C suggests twenty nine which produces an incorrect ratio when tested in the formula. Option D suggests two hundred ninety five which vastly exceeds the solution bounds.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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