dane są liczby a=2-√3, b=3+2√3   oblicz: a-b, a*b , a/b, 1/a, a2   usun niewymiernosc z mianownika 8/√2 , 7/3√3

a - b = [latex](2 - sqrt{3}) - (3 + 2sqrt{3}) = 2 - sqrt{3} - 3 - 2sqrt{3} = - 1 - 3sqrt{3}[/latex] a*b = [latex](2 - sqrt{3})*(3 + 2sqrt{3}) = 6 + 4sqrt{3} - 3sqrt{3} -6 = sqrt{3}[/latex] a/b = [latex]frac{2 - sqrt{3}}{3 + 2sqrt{3}} = frac{(2 - sqrt{3})(3 - 2sqrt{3})}{(3 + 2sqrt{3})(3 - 2sqrt{3})} = frac{6 - 4sqrt{3} - 3sqrt{3} + 6}{3^2 - (2sqrt{3})^2} = frac{12 - 7sqrt{3}}{9 - 12} = frac{7sqrt{3}}{3} - 4[/latex] 1/a = [latex]frac{1}{2 - sqrt{3}} = frac{2 + sqrt{3}}{(2 - sqrt{3})(2 + sqrt{3})} = frac{2 + sqrt{3}}{2^2 - (sqrt{3})^2} = frac{2 + sqrt{3}}{4 - 3} = 2 + sqrt{3}[/latex] a2 = [latex](2 - sqrt{3})^2 = 2^2 - 2*2*sqrt{3} + (sqrt{3})^2 = 4 - 3sqrt{3} + 3 = 7 - 3sqrt{3}[/latex] 8/√2 = [latex]frac{8}{sqrt{2}} = frac{8sqrt{2}}{(sqrt{2})^2} = frac{8sqrt{2}}{2} = 4sqrt{2}[/latex] 7/3√3 = [latex]frac{7}{3sqrt{3}} = frac{7sqrt{3}}{3(sqrt{3})^2} = frac{7sqrt{3}}{9}[/latex]   jak masz pytania to pisz na pw

a=2-√3, b=3+2√3   a-b 2-√3 - ( 3+2√3 ) = 2- √3 - 3 - 2√3 = -1 -3√3   a*b   (2-√3)(3 + 2√3) = 6 +4√3 -3√3 -6 = √3   a/b (2-√3)/ (3+2√3)=(2-√3)/(3+2√3)* (3-2√3 )/ (3-2√3)= (6-4√3 -3√3 +6) / (9-12) = =(12-7√3)/-3   1/a 1/(2-√3) = 1/ (2-√3)* (2+√3)/(2+√3)=2+√3   a² (2-√3)²= 4 - 4√3 + 3 = 7 -4√3     8/√2 =8/√2 *√2/√2= 8√2/2=4√2   7/3√3=7/(3√3)*(3√3)/(3√3)=21√3/27=7√3/9