SOLUTION: Find the value of (a+b)/(a-b) if (a+b)^2 = 8ab and a^2 + b^2 = 6ab. a and b are real numbers

So as we see, the two equations are equivalent.
So there was no need for both those equivalent
equations to have been given.  Just one of them
was all that was necessary.

So we just solve for one of the variables in 
terms of the other:



That's a quadratic in two variables.
It is symmetrical in a and b. 

Solving for a in terms of b. To avoid a conflict
of letters, we CAPITALIZE the letters of the 
quadratic formula



















Now we want to find











We rationalize the denominator:


3b ± 2√2b + b
————————————— =
3b ± 2√2b - b


4b ± 2√2b
————————— =
2b ± 2√2b

 
2 ± √2
—————— =
1 ± √2


(2 ± √2)(1 ∓ √2)
———————————————— =
(1 ± √2)(1 ∓ √2)


2 ± √2 ∓ √2 - 2
———————————————— =
1 ± √2 ∓ √2 - 2


∓√2
——— =
-1


±√2


Edwin

Instead of , let us consider the square of this expression,

.  

It is   =    ( <--- I replaced  in the numerator by  8ab  according to the condition )

=  =                    ( <--- I replaced  in the denominator by  6ab  according to the condition )

=  = 2.


Since the square of the expression is equal to 2, the expression itself is +/-:

 = +/-.