Question

Media aritmetica a numerelor √7 - 4 √3 (la inceput e un radical mare) si √7 + 4 √3 este..

Answer 1

Se foloseste formula radicalilor compusi:
[tex] \sqrt{7-4\sqrt3}=\sqrt{7-\sqrt{4^2*3}}= \sqrt{7-\sqrt{48}} \\ \\ C= \sqrt{7^2-48}=\sqrt{1}=1 \\ \\ \sqrt{7-4\sqrt3}= \sqrt{ \frac{7+1}{2}}- \sqrt{ \frac{7-1}{2}}= \sqrt{4}- \sqrt{3} =2- \sqrt{3}$(2- \sqrt{3}+ 2+\sqrt{3}):2=4:2=2$[/tex]

$\sqrt{7+4\sqrt3}=\sqrt{7+\sqrt{4^2*3}}= \sqrt{7+\sqrt{48}} \\ \\ C= \sqrt{7^2-48}=\sqrt{1}=1 \\ \\ \sqrt{7+4\sqrt3}= \sqrt{ \frac{7+1}{2}}+ \sqrt{ \frac{7-1}{2}}= \sqrt{4}+ \sqrt{3} = 2+\sqrt{3}$

Media aritmetica a celor doi radicali mari este suma radicalilor supra 2= (2-√3+2+√3):2=4:2=2