Question

Stiind ca $\frac{a}{b}$ = $\frac{2}{5}$ si $\frac{b}{c}$ = $\frac{3}{4}$ , sa se calculeze E=$\frac{ a^{2} }{bc}$+$\frac{ b^{2} }{ac}$+$\frac{ c^{2} }{ab}$
Va rog ajutati-ma!

Answer 1

Inmultim cele 2 rapoarte
$\frac{a}{b}*\frac{c}{a}=\frac{a}{c}=\frac{2}{5}*\frac{3}{4}=\frac{3}{10}$
Si vedem si rapoartele inversate ce valori au
$\frac{b}{a}=\frac{5}{2}$
$\frac{c}{b}=\frac{4}{3}$
$\frac{c}{a}=\frac{10}{3}$
Si acum putem sa calculam expresia
$E=\frac{a*a}{b*c}+\frac{b*b}{a*c}+\frac{c*c}{a*b}=\frac{a}{b}*\frac{a}{c}+\frac{b}{a}*\frac{b}{c}+\frac{c}{a}*\frac{c}{b}=\frac{2}{5}*\frac{3}{10}+\frac{5}{2}*\frac{3}{4}+\frac{10}{3}*\frac{4}{3}=\frac{3}{25}+\frac{15}{8}+\frac{40}{9}=\frac{3*8*9}{25*8*9}+\frac{15*9*25}{<span>25*8*9</span>}+\frac{40*25*8}{25*8*9}=\frac{216+3375+8000}{1800}=\frac{11591}{1800}$