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
