Question

Calculati media geometrica si media aritmetica a numerelor:
ma intereseaza punctele a,b,c .

Answer 1

Răspuns:

a) x= $\sqrt{(2\sqrt{5}-6)^{2} }$ = 6-$2\sqrt{5}$

y = $2\sqrt{5}$ +6

Ma = (x+y)/2 = (6-$2\sqrt{5}$+ $2\sqrt{5}$ +6)/2 = 12/2 = 6

Mg = $\sqrt{x*y}$ = $\sqrt{(6-2\sqrt{5})(2\sqrt{5}+6) }$ = $\sqrt{36-20}$ = $\sqrt{16}$ = 4

b) La x

Amplifici 2/($\sqrt{5}$+$\sqrt{3}$) cu $\sqrt{5}$ - $\sqrt{3}$

⇒ x = 2($\sqrt{5}$-$\sqrt{3}$)/2+$\sqrt{3}$-1

Simplifici 2 cu 2

⇒ x = $\sqrt{5}$ - $\sqrt{3}$ + $\sqrt{3}$-1

-$\sqrt{3}$ si +$\sqrt{3}$, se reduc

⇒ x = $\sqrt{5}$-1

La y, amplifici fractia cu $2\sqrt{2}$+$\sqrt{5}$

⇒ y = $2\sqrt{2}$+$\sqrt{5}$

Ma = (x+y)/2 = ($\sqrt{5}$-1+$2\sqrt{2}$+$\sqrt{5}$)/2 = ($2\sqrt{5}$-1+$2\sqrt{2}$)/2

Mg = rad din $2\sqrt{10}$+5-$2\sqrt{2}$-$\sqrt{5}$