SOLUTION: How do solve this word problem as a polynomial equation? The sum of two numbers is 13 and the sum of their squares is 85. Find the numbers.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do solve this word problem as a polynomial equation? The sum of two numbers is 13 and the sum of their squares is 85. Find the numbers.      Log On


   

Question 118301: How do solve this word problem as a polynomial equation?
The sum of two numbers is 13 and the sum of their squares is 85. Find the numbers.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system
x%2By=13
x%5E2%2By%5E2=85



y=13-x Subtract x from both sides for the first equation to solve for y


x%5E2%2B%2813-x%29%5E2=85 Plug in y=13-x into the second equation


x%5E2%2B169-26x%2Bx%5E2=85 Foil


x%5E2%2B169-26x%2Bx%5E2-85=0 Subtract 85 from both sides


2x%5E2-26x%2B84=0 Subtract 85 from both sides




2%28x-7%29%28x-6%29=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-7=0 or x-6=0

x=7 or x=6 Now solve for x in each case


So our answer is
x=7 or x=6


Now take the first answer x=7 and plug it into y=13-x

y=13-7 Plug in x=7

y=6 Subtract


So one pair of numbers is 7 and 6

---------


Now take the second answer x=6 and plug it into y=13-x

y=13-6 Plug in x=6

y=7 Subtract


So one pair of numbers is 6 and 7 (notice how the order of the numbers has changed but the numbers themselves are the same).



---------------------------
Answer:
So the two numbers are:

6 and 7