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.Com
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) (Show Source): You can put this solution on YOUR website!
Start with the given system
Subtract x from both sides for the first equation to solve for y
Plug in into the second equation
Foil
Subtract 85 from both sides
Subtract 85 from both sides
Factor the left side (note: if you need help with factoring, check out this solver)
Now set each factor equal to zero:
or
or Now solve for x in each case
So our answer is
or
Now take the first answer and plug it into
Plug in
Subtract
So one pair of numbers is 7 and 6
---------
Now take the second answer and plug it into
Plug in
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
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