Solve the following system in R: {y/x+x/y=17/4, x^2-y^2=25

drobtinicnu

drobtinicnu

Answered question

2022-09-07

Solve the following system in R :
  { y x + x y = 17 4 x 2 y 2 = 25

Answer & Explanation

yamalwg

yamalwg

Beginner2022-09-08Added 17 answers

Let s = x y and t = x + y. Then the first equation becomes
t s t + s + t + s t s = 17 4
which with some manipulation becomes 9 t 2 = 25 s 2 , or equivalently t = ± 5 3 s.
The second equation is s t = 25. The rest should not be difficult.
ymochelows

ymochelows

Beginner2022-09-09Added 2 answers

Multiplying by 4 x y gives 4 x 2 + 4 y 2 = 17 x y or 4 x 2 17 x y + 4 y 2 = 0, so ( 4 x y ) ( x 4 y ) = 0..
Now substitute y = 4 x and x = 4 y into the second equation to find the possible solutions.

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