Welcome to the article The sum of the squares of two consecutive natural numbers is 313 Find the numbers. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!
Answer :
Answer:
Set one: 12 and 13
Set two: -13 and - 12
Step-by-step explanation:
Let the smaller number = x
Let the larger number = x + 1
x^2 + (x + 1)^2 = 313 Remove the brackets on the left.
x^2 + (x^2 + 2x + 1) = 313
x^2 + x^2 + 2x + 1 = 313 Collect like terms
2x^2 + 2x + 1 = 313 Subtract 313 from both sides
2x^2 + 2x + 1 - 313 = 313 - 313
2x^2 + 2x - 312 = 0 Divide by 2
x^2 + x - 156 = 0
factor
There are two sets of factors that work
Set One
x = 12
x + 1 = 13
Set Two
x = - 13
x+1 = -13 + 1 = - 12
The second set is where you will get your marks. Few people will remember to use the minus answer
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Rewritten by : Brahmana