SOLUTION: the sum of two numbers is 210. if one number is the square of the other, find the set of numbers

Question 887872: the sum of two numbers is 210. if one number is the square of the other, find the set of numbers

Found 2 solutions by DrBeeee, rothauserc:
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let x,y be the unknown numbers.
We are given
(1) x + y = 210
(2) x = y^2
Put (2) into (1) and get
(3) y^2 + y = 210 or
(4) y^2 + y - 210 = 0
This factors into
(5) (y-14)*(y+15) = 0 giving us two values of y
(6) y = {14,-15)
Now use (2) to get the corresponding values of x as
(7) x = {196,225}
Let's check this with (1).
Is (196 + 14 = 210)?
Is (210 = 210)? Yes
Is (225 + (-15) = 210)?
Is (210 = 210)? Yes
Answer; There are two pairs of numbers (196,14) and (225,-15).
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
x +y = 210
y = x^2
substitute for y in first equation
x^2 +x -210 = 0
factor equation
(x+15)*(x-14) = 0
x = -15 or 14
y = 225 or 196
solution1 is x = -15, y = 225
solution2 is x = 14, y = 196

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