Question

Упростить вырожение а) (1+√5)^2 б) (√5-√3)(√5+√3) в) (3√14+√7):√7-2√2;

Answer 1

$(1+\sqrt{5})^2=1^2+2*1*\sqrt{5}+(\sqrt{5})^2=1+2\sqrt{5}+5=6+2\sqrt{5}\\\\(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})=(\sqrt{5})^2-(\sqrt{3})^2=5-3=2\\\\\frac{3\sqrt{14}+\sqrt{7}}{\sqrt{7}}-2\sqrt{2}=\frac{\sqrt{7}(3\sqrt{2}+1)}{\sqrt{7}}-2\sqrt{2}=3\sqrt{2}+1-2\sqrt{2}=\sqrt{2}+1$

Формулы для решения:

$(a+b)^2=a^2+2ab+b^2\\\\(a-b)(a+b)=a^2-b^2$