3 no.s are in the ratio 2:3:4 the sum of their cubes is 33957 find the no.s
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let the numbers be (2x^3)+(3x^3)+(4x^3)
so,
(2x^3)+(3x^3)+(4x^3)=33957
8x^3+27x^3+64x^3=33957
(8x+27x+64x)^3=33957
99x^3=33957
x^3=33957÷99
x^3=343
x=cube root of 343
i.e x=7
the numbers are 7×2=14; 7×3=21;7×4=28
so,
(2x^3)+(3x^3)+(4x^3)=33957
8x^3+27x^3+64x^3=33957
(8x+27x+64x)^3=33957
99x^3=33957
x^3=33957÷99
x^3=343
x=cube root of 343
i.e x=7
the numbers are 7×2=14; 7×3=21;7×4=28
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