Math Problem Statement
Solution
The problem in the image reads:
"The sum of the squares of two consecutive even natural numbers is 100. Find the numbers."
Let's solve this step-by-step:
- Let the two consecutive even natural numbers be and .
- The square of is and the square of is .
- According to the problem, the sum of these squares is 100:
- Expanding :
- Combining like terms:
- Subtracting 100 from both sides:
- Dividing the entire equation by 2:
- Now, we can factor this quadratic equation:
- Setting each factor to zero gives:
- So, the two consecutive even natural numbers are and .
Answer: The two consecutive even natural numbers are 6 and 8.
Would you like further details or explanations on this solution?
Here are five related questions you might find helpful:
- What are other methods to solve quadratic equations like factoring, completing the square, or using the quadratic formula?
- How can we identify whether numbers are consecutive even numbers in a sequence?
- How do we solve similar problems with consecutive odd numbers instead of even?
- What are some practical applications of solving equations involving sums of squares?
- How do we check if our solution satisfies the original problem conditions?
Tip: When solving problems involving consecutive numbers, assigning variables strategically (like and for even numbers) helps simplify equations and ensure accuracy.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Formulas
Sum of squares formula: x^2 + (x+2)^2 = 100
Quadratic equation: ax^2 + bx + c = 0
Theorems
Factoring method for solving quadratic equations
Suitable Grade Level
Grades 8-10
Related Recommendation
Solve for Consecutive Even Numbers with Sum of Squares Equal to 100
Finding Two Consecutive Negative Even Integers Whose Sum of Squares is 100
Find Three Consecutive Integers with Sum of Squares Equal to 110
Find the Two Consecutive Even Integers with a Difference of Squares Equal to 68
Solve a Quadratic Equation Involving Sum of a Number and Its Next Multiple