The sum of two positive numbers equals the difference of the squares of the two numbers which equals the quotient of the...

Question

The sum of two positive numbers equals the difference of the squares of the two numbers which equals the quotient of the larger number when divided by the smaller. What is the smaller number?

 

 

I know that the formula is a+b=a^2+b^2=a/b

but i am not sure where to go from there. Please help meeee!!!!!!!!!!!!

Answer 1

 

The key to starting this one is recognizing that you can factor the difference of two squares.

 

Taking the first part of the relationship:

a+b =  a^2 - b^2   (you goofed on the sign here!)

 

You can factor the difference of two squares, so:

a+b = (a+b)(a-b)

divide both sides by (a+b)

1 = a-b

a = b+1

(and a is the larger number!)

 

Now, using the first and third parts of the relationship:

a+b = a/b

Substitute (b+1) for a:

b+1+b = (b+1) / b

2b + 1 = (b+1) / b

2b^2 + b = b + 1

2b^2 = 1

b = √(1/2) = (√2) / 2

 

a = 1 + (√2) / 2

 

You can check all three terms to make sure they're equal.  It's a bit messy, but each one equals 1 + √2.