Question 733314: find two consecutive positive integers such that the sum of their squares is 61 Found 2 solutions by josmiceli, rothauserc:Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! Call the consecutive integers and
given:
Looking at this, I see that and the difference is ,
so my guess is:
I need the positive solution
The consecutive numbers are 5 and 6
check:
OK
You can put this solution on YOUR website! let i represent a positive integer and i+1 be the consecutive integer. We know that
i squared + (i+1)squared = 61
squaring both terms
i squared + i squared + 2i + 1 = 61
combining terms and subtracting 1 from both sides of equal sign we have
2 i squared + 2i = 60
divide equation by 2
i squared + i = 30
we now have the quadratic equation
i squared + i - 30 = 0
factoring the quadratic equation, we have
( i + 6 ) * (i - 5) = 0
this gives us two equations
i + 6 = 0 and i - 5 = 0
now the integers are required to be positive so the solution is
i = 5 and i+1 = 6
and we see that
5 squared + 6 squared = 61
namely,
25 + 36 = 61
