SOLUTION: Good day Here's my question. It's listed under "Establishing quadratic equations from word problems" The sum of two integers is 5. The difference between their squares is 45.

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Question 893882: Good day
Here's my question. It's listed under "Establishing quadratic equations from word problems"
The sum of two integers is 5. The difference between their squares is 45. What are the numbers?
I don't know how to start.
Kind Regards
Found 2 solutions by Theo, Fombitz:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
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.

Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
First translate the words into math equations.
1. "sum of two integers is 5"
2. "difference between their squares is 45"
From eq. 1,

Substitute into eq. 2,

Then,