Gr a (3-√5)(4-2√5)=12-6√5-4√5+10=22-10√5 (3-√5)/(4-2√5) *(4+2√5)(4+2√5)=(2+2√5)/(16-20)=-(1+√5)/2 (4-2√5)²=16-20=-4
[latex]A.\x = 3-sqrt{5}\y = 4-2sqrt{5}\\xy = (3-sqrt{5})(4-2sqrt{5})=12-6sqrt{5}-4sqrt{5}+10=22-10sqrt{5}[/latex] [latex]frac{x}{y} = frac{3-sqrt{5}}{4-2sqrt{5}}cdotfrac{4+2sqrt{5}}{4+2sqrt{5}} = frac{(3-sqrt{5})(4+2sqrt{5})}{16-20} = frac{12+6sqrt{5}-4sqrt{5}-10}{-4}=frac{2+2sqrt{5}}{-4}=\\=frac{-2(1+sqrt{5})}{4} = frac{-1-sqrt{5}}{2}[/latex] [latex]y^{2} = (4-2sqrt{5})^{2}=4^{2}-2cdot4cdot2sqrt{5}+(2sqrt{5})^{2} = 16-16sqrt{5}+20=\\=36-16sqrt{5}[/latex] [latex]B.\x = 2+sqrt{3}\y = 3-2sqrt{3}\\xy = (2+sqrt{3})(3-2sqrt{3}) = 6-4sqrt{3}+3sqrt{3}-6=-sqrt{3}[/latex] [latex]frac{x}{y} = frac{2+sqrt{3}}{3-2sqrt{3}}cdotfrac{3+2sqrt{3}}{3+2sqrt{3}}=frac{(2+sqrt{3})(3+2sqrt{3})}{9-12}=frac{6+4sqrt{3}+3sqrt{3}+6}{-3}=frac{-12-7sqrt{3}}{3}[/latex] [latex]y^{2} = (3-2sqrt{3})^{2} = 3^{2}-2cdot3cdot2sqrt{3}+(2sqrt{3})^{2}=9-12sqrt{3}+12=\\=21-12sqrt{3} = 3(7-4sqrt{3})[/latex]
