The sum of the squares of two consecutive positive odd numbers is 2314. What is the smaller number?
Answer and explanation
Correct answer: 33
Let the smaller number be x. The next consecutive odd number is x+2. Thus, \(x^2+(x+2)^2=2314\), which simplifies to \(2x^2+4x-2310=0\) or \(x^2+2x-1155=0\). Factoring gives \((x-33)(x+35)=0\). Since the numbers are positive, \(x=33\) is valid, while \(x=-35\) is not. Therefore, the correct answer is 33. Exam tip: For consecutive odd numbers, use a difference of 2 and reject any non-positive root.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
Let the smaller number be x. The next consecutive odd number is x+2. Thus, \(x^2+(x+2)^2=2314\), which simplifies to \(2x^2+4x-2310=0\) or \(x^2+2x-1155=0\). Factoring gives \((x-33)(x+35)=0\). Since the numbers are positive, \(x=33\) is valid, while \(x=-35\) is not. Therefore, the correct answer is 33. Exam tip: For consecutive odd numbers, use a difference of 2 and reject any non-positive root.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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