Question

Cat este parte intreaga a nr
a) $\sqrt{4n^{2}+ 4n}$
b) $\sqrt{16n^{2}+ 8}$ (va rog frumos sa imi explicati cum se fac)

Answer 1

a) $4n^2+4n\ \textless \ (2n+1)^2 \ \textless \ =\ \textgreater \ 4n^2+4n\ \textless \ 4n^2+4n+1 (adevarat)$ (1)
$(2n)^2 \leq 4n^2+4n \ \textless \ =\ \textgreater \ 4n^2 \leq 4n^2+4n (adevarat)$(2)
din (1) si (2) => $(2n)^2 \leq 4n^2+4n\ \textless \ (2n+1)^2 \ \textless \ =\ \textgreater \ 2n \leq \sqrt{4n^2+4n} \ \textless \ 2n+$