perplexus.info :: Just Math : Absolute Rational Relations

Absolute Rational Relations (Posted on 2024-05-20)

Let a and b be real numbers such that:

a/b + b/a = 13/6

Find the value of

|(a + b)/(a - b)|

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 4.0000 (1 votes)

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Puzzle Answer_Method 1

| Comment 1 of 3

Method 1

---------------

a/b + b/a = 13/6

=> (a^2 + b^2)/(a.b)= 13/6

=> (a^2+b^2+2ab)/(a^2+b^2-2ab) = (13+12)/(13-12)

=> [(a+b)/(a-b)]^2 = 25

=> (a+b)/(a-b) = +/- 5

=> |(a+b)/(a-b)| = 5

Posted by K Sengupta on 2024-05-20 07:37:07

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