SOLUTION: One positive number is 5 more than another. The sum of their squares is 53. Find BOTH numbers and solve algebraically.

Algebra ->  Equations -> SOLUTION: One positive number is 5 more than another. The sum of their squares is 53. Find BOTH numbers and solve algebraically.      Log On


   

Question 252851: One positive number is 5 more than another. The sum of their squares is 53. Find BOTH numbers and solve algebraically.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x=y+5
x^2+y^2=53
They must be rather small numbers if their sum is 53 since 7^2=49
and it just so happens that 2 and 7 are the numbers
2^2+7^2=53
7-2=5
so now you have 4the equations to solve it and the answers.
there is a good chance that you can factor the equation
just plug y+5 in for x in the equation x^2+y^2=53
(y+5)^2+y^2=53
y^2+10y+25+y^2=53
2y^2+10y-28=0
divide by 2
y2+5y-14=0
Yes it can be factored
(y+7)(y-2)==
y=-7
y=2
discard the -7 since we need a positive result
x=y+5
x=7
we already showed that 2 and 7 work