Solve x y = 3 and 4 x 2 </msup> </msup> +

Laylah Mora

Laylah Mora

Answered question

2022-05-20

Solve x y = 3 and 4 x 2 + 2 y 2 = 72

Answer & Explanation

nifeonibonitozg

nifeonibonitozg

Beginner2022-05-21Added 12 answers

The first attempt to try to solve a system of two (or more variables) is naturally assumed that a possible solution is one in which all variables are equal.
Then set x = y = t and solve de equation
{ x y = t t = 3 4 x 2 + 2 y 2 = ( 2 t 2 ) 2 + 2 t 2 = 72
By t 2 = 3 we have t = ± 3 . Substituting into the another equation we have that two solutions are ( x , y ) = ( + 3 , + 3 ) and ( x , y ) = ( 3 , 3 ). Or by ( 2 t 2 ) 2 + 2 t 2 = 72 whe have 2 t 2 = 1 + 289 2 = 8.
To further investigate other solutions you might assume
x = t + s , y = t s .

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