Solve { <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd>

Davon Irwin

Davon Irwin

Answered question

2022-06-25

Solve
{ 5 a 2 4 a b b 2 + 9 = 0 21 a 2 10 a b + 40 a b 2 + 8 b 12 = 0.

Answer & Explanation

Brendon Fernandez

Brendon Fernandez

Beginner2022-06-26Added 14 answers

You can notice that many terms of
( b + 5 a 4 ) 2 = b 2 + 10 a b 8 b 40 a + 25 a 2 + 16
appear in the first equation. Similarly, in the first one, you can notice ( b + 2 a ) 2 .
By algebraic manipulation you get that the original equations are equivalent to
( b + 5 a 4 ) 2 = 4 ( a 2 + 1 ) ( b + 2 a ) 2 = 9 ( a 2 + 1 )
which implies 4 ( b + 2 a ) 2 = 9 ( b + 5 a 4 ) 2 and 2 ( b + 2 a ) = ± 3 ( b + 5 a 4 ). This should simplify things a little. (In each of the two possibilities you can express b using a as a linear expression. Then you will get a quadratic equation in a. Or you can start by eliminating
migongoniwt

migongoniwt

Beginner2022-06-27Added 4 answers

By arrange the terms, you can note that
{ 5 a 2 4 a b b 2 + 9 = 0 21 a 2 10 a b + 40 a b 2 + 8 b 12 = 0 { 9 ( a 2 + 1 ) = ( 2 a + b ) 2 4 ( a 2 + 1 ) = ( 5 a + b 4 ) 2
So we get
{ 9 ( a 2 + 1 ) = ( 2 a + b ) 2 4 ( 2 a + b ) 2 = 9 ( 5 a + b 4 ) 2
According to the second equation, we can get two cases of first relation between a and b, then substitute them into the first equation respectively, we can get all the cases of values of pairs ( a , b ).

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?