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 2 of 3 |

Method 2

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

Let a/b = p

Then, by the given conditions:

p+1/p =13/6

--> 6(p^2+1) =13p

--> 6p^2-13p+6 =0

--> 6p^2-9p -4p+6 =0

--> 3p(2p-3) -2(2p-3) =0

--> (2p-3)(3p-2) =0

--> p =3/2, 2/3

If p= 3/2

--> a/b = 3/2

--> (a+b)/(a-b) = (3+2)/(3-2) (By componendo and dividendo)

--> (a+b)/(a-b) = 5/1

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

If a/b = 2/3

--> (a+b)/(a-b) = 5/-1

--> (a+b) /(a-b) = -5/1

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

Therefore, |(a + b)/(a - b)| =5

Consequently, |a + b)/(a - b)| =5

Edited on May 20, 2024, 7:38 am

Posted by K Sengupta on 2024-05-20 07:37:57

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