Question

Three numbers are to one another 2:3:4. The sum of their cubes is 33957. Find the numbers.

Solution

Let the numbers be 2x, 3x and 4x sum of cubes = 33957 ⇒(2x)³ + (3x)³ + (4x)³ = 33957 ⇒8x³ + 27x³ + 64x³ = 33957 ⇒99x³ = 33957 ⇒x³ = 33957/99 = 343 ⇒x = ∛343 = 7 Numbers are: 2x = 2×7 = 14 3x = 3×7 = 21 4x = 4×7 = 28

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