Question

Combinari de n luate cate 2 = 28, n apartine N nr naturale, nmai mare sau egal cu 2

Answer 1

$C_n^2=28,\;sau\;\dfrac{n!}{2!\cdot(n-2)!}=28,\;sau\dfrac{n\cdot(n-1)\cdot(n-2)!}{2\cdot(n-2)!}=28,\;sau\\\\n\cdot(n-1)=56\to n^2-n-56=0;\\\\\Delta=b^2-4ac=(-1)^2-4\cdot1\cdot(-56)=225\to\sqrt{\Delta}=15;\\\\n_{1,2}=\dfrac{-b\pm\sqrt{\Delta}}{2\cdot a}=\dfrac{-(-1)\pm 15}{2}\to n_1=-7\;si\;n_2=8.$

Singura soluţie care convine este n = 8.

Green eyes.