Solve the system of equations: { <mtable columnalign="left left" rowspacing=".2em" colu

Kaeden Woodard

Kaeden Woodard

Answered question

2022-05-27

Solve the system of equations:
{ x 2 + x y + y 2 x 2 + y 2 + 1 = 1 x y ( 3 + x y ) log 2 x + x ( 3 x y ) log 2 y = 1 + x y

Answer & Explanation

Julien Carrillo

Julien Carrillo

Beginner2022-05-28Added 13 answers

Subsitute x y = 1 , y = 1 / x , a n d l o g y = l o g x:
l o g ( 3 1 / 2 + 1 ) l o g x + x l o g ( 3 1 / 2 1 ) l o g x = 1 + x 2
then take Log at both sides of your equation then your 2nd equation becomes
l o g x l o g ( 3 1 / 2 + 1 ) + l o g x + l o g x l o g ( 3 1 / 2 1 ) = 2 l o g x
l o g ( 3 1 / 2 + 1 ) + l o g ( 3 1 / 2 1 ) = 1
l o g ( ( 3 1 / 2 + 1 ) ( 3 1 / 2 1 ) ) = 1
which is always true!

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?