Cubes

Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.

Result

a =  87 dm
b =  39 dm

Solution:

 ab=48 6a26b2=36288 (48+b)2b26048=0 b=6048482248=87 a=48+b=39 \ \\ a-b = 48 \ \\ 6a^2-6b^2=36288 \ \\ (48+b)^2-b^2-6048 =0 \ \\ b = \dfrac{ 6048-48^2}{ 2\cdot 48} = 87 \ \\ a = 48 + b= 39



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