Question

1.)Aratati ca daca $\frac{a}{2}$=$\frac{b}{3}$=$\frac{c}{5}$ , atunci $(a+b-c)^{2013} =0$

2.)Determinati numerele naturale x y si z astfel incat urmatoarele fractii sa fie echivalente :
$\frac{3}{2}$ ; $\frac{2x+7}{10}$ ; $\frac{24}{3z+1}$

Answer 1

1. a/2=b/3=c/5=k;
⇒a=2k;
⇒b=3k;
⇒c=5k;
⇒[2k+3k-5k]²⁰¹³=0²⁰¹³=0;
2. 3/2=2x+7/10
⇒4x+14=30⇒4x=16⇒x=4;
⇒15/10=24/3z+1
⇒45z+15=240
⇒45z=225⇒z=5;
⇒x=4;
⇒z=5;