The sum of the squares of three consecutive even natural numbers is 1460. Find the numbers.
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Answer: B. 20, 22, 24
Explanation
Expressing three consecutive even numbers as x minus two, x, and x plus two simplifies the algebraic sum. Expanding and adding their squares results in a simplified quadratic equation equal to three times x squared plus eight. Solving the equation yields an x value of twenty-two, which generates the correct number sequence of 20, 22, and 24. Consecutive even natural numbers differ from each other by a constant difference of exactly two units. Quadratic equations can be solved by isolating the squared variable term and taking the square root of both sides. The sum of squares method is commonly used to find unknown numbers when their sequential relationships are known.
Option A yields a sum of squares that is too small when calculated using the same algebraic method. Option C produces a sum of squares that exceeds the target value of 1460 specified in the problem. Option D represents a higher sequence of consecutive even numbers whose squared sum is significantly greater than 1460.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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