Farewell photos

At the end of the school year, ninth-grade boys and girls said goodbye by exchanging photos with each other. A total of 552 photos were exchanged. How many students were there?

Final Answer:

n =  24

Step-by-step explanation:

$$\begin{gathered} n\cdot (n-1)=552 \\ n\cdot (n-1)=552 \\ {n}^2-n-552=0 \\ a=1;b=-1;c=-552 \\ D=b^2-4ac=1^2-4\cdot 1\cdot (-552)=2209 \\ D>0 \\ {n}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{1\pm \sqrt{2209}}{2} \\ {n}_{1,2}=\frac{1\pm 47}{2} \\ {n}_{1,2}=0.5\pm 23.5 \\ {n}_1=24 \\ {n}_2=-23 \\ n>0 \\ n=n_1=24 \\ f=n\cdot (n-1)=24\cdot (24-1)=552 \end{gathered}$$

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