The sum of squares of two consecutive positive integers exceeds their product by 91. Find the integers.
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Answer: A. 9, 10
Explanation
Representing the two consecutive positive integers as x and x plus one sets up the required algebraic equation. Squaring both integers and subtracting their product yields an expression that simplifies to a quadratic equation. Solving the resulting quadratic equation yields x equal to nine, making the integers nine and ten. Consecutive integers follow one another in order without gaps, differing by exactly one unit in numerical value. Quadratic equations contain variables raised to the second power and can be solved through factoring or formula methods. Positive integers are whole numbers greater than zero that exclude negative values and fractional quantities.
Ten and eleven yield a sum of squares and product difference that equals one hundred eleven instead of ninety one. Eleven and twelve produce a significantly larger result that exceeds the target value specified in the problem statement. Twelve and thirteen result in an even higher calculation value that does not satisfy the given mathematical condition.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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