Question

poate cineva sa ma ajute la acest exercitiu?

Answer 1

   
[tex]\displaystyle\\ f(x)=x+ \frac{1}{2} \\\\ f\left(- \frac{17}{2} \right)\cdot f\left(- \frac{15}{2} \right)\cdot ... \cdot f\left(\frac{21}{2} \right) = ?\\\\ \text{La numarator avem numere intregi impare consecutive}\\ \text{de la -17 pana la 21.}\\\\ \{-17;~-15;~-13;~-11;~-9;~-7;~-5;~-3;~-1;~1;~3;~5;\\\\ 7;~9;~11;~13;~15;~17;~19;~21\}\\\\ f\left(- \frac{17}{2} \right)\cdot f\left(- \frac{15}{2} \right)\cdot ... \cdot f\left(- \frac{1}{2} \right)\cdot ... \cdot f\left(\frac{21}{2} \right) = [/tex]


[tex]\displaystyle\\ =\left(-\frac{17}{2}+ \frac{1}{2} \right)\cdot \left(-\frac{15}{2}+ \frac{1}{2} \right)\cdot ... \cdot \underbrace{\left(-\frac{1}{2}+\frac{1}{2}\right)}_{=~0}\cdot ... \cdot \left(\frac{21}{2}+ \frac{1}{2} \right) =\\\\\\ =\left(-\frac{17}{2}+ \frac{1}{2} \right)\cdot \left(-\frac{15}{2}+ \frac{1}{2} \right)\cdot ... \cdot 0\cdot ... \cdot \left(\frac{21}{2}+ \frac{1}{2} \right) =0\\\\ \text{Observam ca unul din factori este egal cu zero.} [/tex]