I dont know how to start....any help is appreciated!!

[z51]

Assume that ߙ a and b are positive real numbers with a not equal to b ,such that: 2a^2 +2b^2= 5ab The value of the expression |(a+b)/(a-b)| is equal to:
Α. 1
Β. 2
c. 3
d. 4
Ε. 5

 

[Deleted member 4993]

Assume that ߙ a and b are positive real numbers with a not equal to b ,such that: 2a^2 +2b^2= 5ab The value of the expression |(a+b)/(a-b)| is equal to:
Α. 1
Β. 2
c. 3
d. 4
Ε. 5

To start you off:

Since a > b and a>0 and b>0 then (a-b)>0............................... continue

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[lex]

Perhaps start by trying to work out [MATH]\ \frac{{(a+b)}^2}{{(a-b)}^2}[/MATH]

 

[JeffM]

An alternative way to start is

[MATH]2a^2 + 2b^2 = 5ab \implies a = \dfrac{-(-5b)\pm \sqrt{(-5b)^2 - 4(2)(2b^2)}}{2 * 2} = \dfrac{5b \pm 3b}{4} \implies[/MATH]
[MATH]a = 0.5b \text { or } a = 2b.[/MATH]
This may relate more obviously to mathematical facts that you already are familiar with.

The main point is: when you are unsure of where to start, try things.