Cubes - diff

The second cube's edge is 2 cm longer than the edge of the first cube. Volume difference blocks are 728 cm³. Calculate the sizes of the edges of the two dice.

Correct answer:

a =  10 cm
b =  12 cm

Step-by-step explanation:

$$\begin{gathered} (a+2{)}^3-a^3=728 \\ (a+2)(a^2+4a+4)-a^3=728 \\ 6a^2+12a+8=728 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{-12\pm \sqrt{17424}}{12} \\ {a}_{1,2}=\frac{-12\pm 132}{12} \\ {a}_{1,2}=-1\pm 11 \\ {a}_1=10 \\ {a}_2=-12 \\ a>0 \\ a=10 \\ b=a+2=12 \end{gathered}$$

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