Solving A+b*sqrt2=c with Positive Rationals

[madah12]

Homework Statement

what's the best way solving question of finding two positive rational a and b given c
where a +b*sqrt2= an irrational number c

Homework Equations

The Attempt at a Solution

 

[epenguin]

when you multiply an irrational number by a rational one, as you are doing here, which type of number is/can be the product? When you add...

Prove it, using the definitions.

 

[HallsofIvy]

In general, such a problem will NOT have a solution. For example, there exist no rational a, b, such that $a+ b\sqrt{2}= \pi$.

 

[epenguin]

In general, such a problem will NOT have a solution. For example, there exist no rational a, b, such that $a+ b\sqrt{2}= \pi$.

I was taking "an irrational number c" to mean some irrational number c in which case there is quite some scope. What math level would be necessary to be able to prove your example?