(1) x+y=23+5+23−5=2(3−5)+2(3+5)(3+5)(3−5)=6−25+6+259−5=3x+y=\dfrac{2}{3+\sqrt{5}}+\dfrac{2}{3-\sqrt{5}}=\dfrac{2\left(3-\sqrt{5}\right)+2(3+\sqrt{5})}{\left(3+\sqrt{5}\right)(3-\sqrt{5})}=\dfrac{6-2\sqrt{5}+6+2\sqrt{5}}{9-5}=3x+y=3+52+3−52=(3+5)(3−5)2(3−5)+2(3+5)=9−56−25+6+25=3 (2) xy=23+5⋅23−5=49−5=1xy=\dfrac{2}{3+\sqrt{5}}\cdot\dfrac{2}{3-\sqrt{5}}=\dfrac{4}{9-5}=1xy=3+52⋅3−52=9−54=1 (3) x2+y2=(x+y)2−2xy=32−2=7x^2+y^2=(x+y)^2-2xy=3^2-2=7x2+y2=(x+y)2−2xy=32−2=7 (4) x3+y3=(x+y)(x2−xy+y2)=3(7−1)=18x^3+y^3=(x+y)(x^2-xy+y^2)=3(7-1)=18x3+y3=(x+y)(x2−xy+y2)=3(7−1)=18