How could I solve (3+4 (sqrt(3)) (x+y (sqrt(3)) =26 for rational x, y ?

[Carrot]

If x and y are rational numbers and (3+4 (sqrt(3)) (x+y (sqrt(3)) =26, find the sum of x and y

 

[tkhunny]

If x and y are rational numbers and (3+4 (sqrt(3)) (x+y (sqrt(3)) =26, find the sum of x and y

Have you considered multiplying the binomials on the left and seeing where it leads?

There is a reason why you were told that x and y are rational.

 

[HallsofIvy]

\(\displaystyle (3+ 4\sqrt{3})(x+ y\sqrt{3})= (3x+ 12y)+ (4x+ 3y)\sqrt{3}= 26\)

Because x and y are rational we must have 3x+ 12y= 26 and 4x+ 3y= 0.