SOLUTION: Find two integers, x and x + 1, whose squares differ by 25.

Question 117950: Find two integers, x and x + 1, whose squares differ by 25.
Found 3 solutions by MathLover1, bucky, jim_thompson5910:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!
two integers;
and , whose squares differ by

and

Answer by bucky(2189)   (Show Source): You can put this solution on YOUR website!
The two unknown integers are represented by x and by x+1
.
If you square the two integers you get:
.

and

.
Squaring results in
.
If you subtract the two squares, the problem tells you that the result is 25. In equation form
this subtraction can be expressed as:
.

.
Notice that in the subtraction the two terms are of opposite sign and therefore
cancel each other. Therefore, you are left with:
.

.
Get rid of the 1 on the left side by subtracting 1 from both sides to get:
.

.
Solve for x by dividing both sides of this equation by 2 to reduce the equation to:
.

.
So one of the unknown integers (that is x) equals 12. The other integer is x + 1 and therefore
it equals 12 + 1 or 13.
.
The two integers you are looking for are 12 and 13.
.
Check. 12 squared is 144 and 13 squared is 169. The difference is 169 - 144 = 25, just as the
problem requires. So this answer checks and the two integers are 12 and 13.
.
Hope this helps you to understand the problem.
.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
If their squares differ by 25, then we have the equation

Start with the given equation

Foil

Combine like terms

Subtract 1 from both sides

Combine like terms on the right side

Divide both sides by 2 to isolate x

Divide

--------------------------------------------------------------
Answer:
So our answer is

Now add 1 to 12 to get the next number. So

This means our two numbers are 12 and 13

Check:

Start with the given equation

Plug in the solution

Square each term

Subtract. Since the two sides of the equation are equal, this verifies our answer.
RELATED QUESTIONS
find two consecutive odd positive integers whose squares differ by... (answered by Alan3354)
Find two numbers whose sum is 10 and whose squares differ by... (answered by checkley75)
Find two integers whose sum is 12 and whose squares differ by 24. Here's what I tried. (answered by richard1234)
Find two integers whose difference is 4 and whose square differ by... (answered by ikleyn,MathTherapy)
find two integers that differ by 6 while their squares differ by 132 (answered by solver91311)
Find two numbers that differ by 6 and whose square roots differ by... (answered by solver91311)
Two positive integers differ by 6 and their squares differ by 72. By how much do their... (answered by JimboP1977)
Find the two consecutive odd integers whose squares differ y... (answered by ankor@dixie-net.com)
Find all pairs of positive integers whose squares differ by... (answered by Edwin McCravy)