[tex]x^{2} =( \sqrt{2}-1) ^{2} =2-2 \sqrt{2}+1=3- 2 \sqrt{2} \\ y= \frac{1}{ \sqrt{2}+1}= \frac{\sqrt{2}-1}{(\sqrt{2}-1)(\sqrt{2}+1)}= \frac{\sqrt{2}-1}{2-1}= \frac{\sqrt{2}-1}{1}= \sqrt{2}-1 \\ x^{2}+y=3- 2 \sqrt{2}+\sqrt{2}-1=2-\sqrt{2} \\ a+b \sqrt{2}=2- \sqrt{2} \\ a+b \sqrt{2}=2+(-1)* \sqrt{2} \\ a=2 \\ b=-1[/tex]
