Question

suma a doua nr rationale nenule este egala cu 61/15, iar produsul lor este egal cu 56/15. Aflati suma inverselor celor doua nr.

Answer 1

a=primul nr
b=al doilea nr 
a+b = $\frac{61}{15}$ 
ab= $\frac{56}{15}$-------->a=$\frac{56}{15b}$

inlocuim a in suma :
$\frac{56}{15b}$ + b =$\frac{61}{15}$  / inmultim toata ecuatia cu 15b
56+15$b^{2}$ = 61b
15$b^{2}$-61b+56=0 
Δ= $61^{2}$-4×15×56
Δ=3721-3360=361----> $\sqrt{Δ}$=19 
b1=$\frac{61+19}{30}$=$\frac{80}{30}$----->a1= $\frac{61}{15} - \frac{80}{30}$=$\frac{122-80}{30}$= $\frac{42}{30}$
b2=$\frac{61-19}{30}$=$\frac{42}{30}$----->a2=$\frac{80}{30}$
suma inverselor nr a1 si b1 : $\frac{30}{42}$ +$\frac{30}{80}$ =$\frac{24000+900}{3360} = \frac{3300}{3360} = \frac{330}{336} = \frac{55}{61}$