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

Răspuns :

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}[tex] (2- \sqrt{3}+ 2+\sqrt{3}):2=4:2=2 [/tex][/tex]

[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}[/tex]

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