How can I solve a system equation with known solution?

[naoufelabs]

Hi,
I have a system equation that I know its solution, but I want the steps that I can solve it:

x*y = 3
4^x2 + 2^y2 = 72

x=y = √3

Thank you.

 

[micromass]

Hi,
I have a system equation that I know its solution, but I want the steps that I can solve it:

x*y = 3
4^x2 + 2^y2 = 72

x=y = √3

Thank you.

First observe that x=0 is not a solution. Then we know that $y=\frac{3}{x}$. Substitute this in the equation
$$4^{x^2}+2^{y^2}=72$$

 

[naoufelabs]

Thanks