Of three

Of three positive numbers the product of the first and second is 42, second and third is 56 and that of third and first is 48. Find the third number.

Final Answer:

c =  8

Step-by-step explanation:

$$\begin{gathered} ab=42 \\ bc=56 \\ ca=48 \\ c(42/b)=48 \\ c(42/(56/c))=48 \\ c\cdot 42/56\cdot c=48 \\ {c}^2=48\cdot 56/42 \\ {c}^2=64 \\ c=\sqrt{64}=8 \\ \text{ Verifying Solution: } \\ b=56/c=56/8=7 \\ a=42/b=42/7=6 \\ {p}_1=a\cdot b=6\cdot 7=42 \\ {p}_2=b\cdot c=7\cdot 8=56 \\ {p}_3=c\cdot a=8\cdot 6=48 \end{gathered}$$

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