Question

Sum of the squares Of two consecutive natural numbers is 313. Find the numbers.

Answer 1

Set one: 12 and 13

Set two: -13 and - 12

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