Question 893882
the sum of 2 integers is equal to 5.
the difference between their squares is 45.


let x equal one of the integers.
let y = the other integer.


the first statement gets you x + y = 5


the second statement gets you x^2 - y^2 = 45


the implicit assumption here is that x will be a larger number than y because x^2 - y^2 = 45.


let's see what we have.


we have:


x + y = 5
x^2 - y^2 = 45.


these are 2 equations that need to be solved simultaneously since we need a solution that is common to both equations.


we will solve for y in terms of x from the first equation.


we get y = 5 - x


we will replace y with 5 - x in the second equation to get:


x^2 - (5-x)^2 = 45


simplify this by performing the indicated operations to get:


x^2 - (25 - 10x + x^2) = 45


simplify by removing parentheses to get:


x^2 - 25 + 10x - x^2 = 45


simplify by combining like terms to get:


-25 + 10x = 45


add 25 to both sides of the equation to get:


10x = 70


divide both sides of the equation by 10 to get:


x = 7


replace x with 7 in the first equation to get 7 + y = 5


solve for y to get y = -2


you have x = 7 and y = -2


replace x with 7 and y with -2 in the second equation to get:


x^2 - y^4 = 45 becomes 7^2 - (-2)^2 = 45 which becomes 49 - 4 = 45 which becomes 45 = 45.


this confirms the solution is good.


your solution is x = 7 and y = -2.


both equations are satisfied with the common solution of x = 7 and y = -2.