# Three numbers are in the ratio 2 3 4 .the sum of their cube is 33957.find the largest number

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by afii

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by afii

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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**

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 =

3x = 3×7 =

4x = 4×7 =

according to problem:

[2x]³+[3x]³+[4x]³=33957

⇒8x³+27x³+64x³=33957

⇒99x³=33957

⇒x³=343

⇒