Sum of the squares of two consecutive natural numbers is 313. find the numbers.

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

glide reflection.

its mainly because the pattern will be infinite and will never end. it will look like a gilder or like a filpbook when set to motion.