Question

9.Calculati media arimetica si media geometrica a numerelor:
a) a=2-√3,
b=2+√3
11.Efectuatii:a)(√5-1)(√5+1)=
b)(2+√3)(2-√3)=
c)(2√3-√5)(2√3+√5)
d)(3 √ 2 - 2 √ 3 ) 3 √ 2 + 2 √ 3)

Answer 1

    
$9) \\ a = 2- \sqrt{3} \\ b= 2+\sqrt{3} \\ M_{a}= \frac{a+b}{2}= \frac{2- \sqrt{3}+2+\sqrt{3}}{2}= \frac{2+2}{2}=\frac{4}{2}=\boxed{2} \\ M_{g}= \sqrt{a*b}= \sqrt{(2- \sqrt{3})*(2+\sqrt{3})} = \\ = \sqrt{2^{2}- (\sqrt{3})^{2}}=\sqrt{4- 3}= \sqrt{1} =\boxed{1}$


$11a) \;\;\; (\sqrt{5}-1)(\sqrt{5}+1)= (\sqrt{5})^{2}-1^{2}=5-1=\boxed{4} \\ 11b)\;\;\;(2+ \sqrt{3} )(2- \sqrt{3})=2^{2}-( \sqrt{3})^{2}=4 - 3 = \boxed{1} \\ 11c)\;\;\;(2 \sqrt{3}- \sqrt{5})(2 \sqrt{3}+ \sqrt{5}))= (2 \sqrt{3})^{2}-(\sqrt{5}))^{2}=12-5=\boxed{7} \\ 11d)\;\;\;(3\sqrt{2}-2 \sqrt{3})(3\sqrt{2}+2 \sqrt{3})=(3\sqrt{2})^{2}-(2\sqrt{3})^{2}=18-12=\boxed{6}$