1) If $x = 1 + \sqrt{2}$ and $y = 1-\sqrt{2}$, find the value of $(x^{2}+y^{2}).$ A) 3 B) 4 C) 5 D) 6 Answer: Option DExplanation:$ (x^{2}+y^{2}) = (1 +\sqrt{2}) + (1 -(\sqrt{2} ^{2}) $$= 2 [1^{2} + \sqrt{2} ^{2}] = 2\times 3 = 6.$