SOLUTION: Let a and b be distinct real numbers for which a/b + (a+10b)/(b+10a) = 2 Find a/b.

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Question 927055: Let a and b be distinct real numbers for which
a/b + (a+10b)/(b+10a) = 2
Find a/b.
Found 2 solutions by CubeyThePenguin, ikleyn:
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
a/b + (a+10b)/(b+10a) = 2

((b)(a+10b)+(a)(10+b))/((b)(b+10a)) = 2

b = 5a/4

a/b = 4/5

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.


            The analysis in the post by  @CubeyThePenguin  is incomplete;

            the answer is incomplete,  too. 


You start from


    a%2Fb + %28a+%2B+10b%29%2F%28b+%2B+10a%29 = 2.


You introduce new variable  x = a%2Fb  (which is under the problem's question).


Then you divide the numerator and the denominator in the given equation by "b".

You will get then this equation for x


    x + %28x%2B10%29%2F%281+%2B+10x%29 = 2.


By multiplying both sides by (1+10x), you get

    x*(1+10x) + (x+10) = 2*(1+10x)

    x + 10x^2 + x + 10 = 2 + 20x

    10x^2 - 18x + 8 = 0


Using the quadratic formula, you get 2 (two, TWO)  roots for x

    x%5B1%5D = 1  and  x%5B2%5D = 4%2F5.


ANSWER.  There are 2 (two, TWO) solutions  a%2Fb = 1  and  a%2Fb = 4%2F5.

Solved (correctly).


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Hello,  @CubeyThePenguin,  consider to hire somebody,  who will assist you by editing / fixing your solutions after you.