SOLUTION: The square of the sum of two numbers is 20 more than the square of their difference. One of the numbers is 1. What is the other number?

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Question 357920: The square of the sum of two numbers is 20 more than the square of their difference. One of the numbers is 1. What is the other number?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Let x represent one of the numbers and  a the other

Questions states

(x+a)^2 = (x-a)^2 +20

let x = 1

%281%2Ba%29%5E2+=+%281-a%29%5E2+%2B+20

1 + 2a + a^2 = 1 -2a + a^2 + 10

4a = 10

a = 10/4 0r 5/2 

checking our answer

(7/2)^2 = (-3/2)^2 + 10

49/4 = 9/4 + 40/4 = 49/4