Question

Three numbers are in the ratio 2:3:4the sum of their cubes 33597 find the cubes

Answer 1

Let the cubes of numbers are 2x3, 3x3  and4x3

(2x)3+ (3x)3+ (4x)3= 33957

8x3 + 27 x 3+ 64x3= 33957

=> 99x3= 33957

=> x3=33957/99

= x3= 343

x=7

The numbers are

 Ist numbe is 2x= 2*7=14

2nd number is 3x = 3*7 = 21

3rd number is 4x = 4*7 = 28

Answer 2

Hey There!!


Three Numbers are in the ratio 2:3:4

So, let the numbers be 2x, 3x and 4x.


Now, sum of cubes is 33597.

So,

$(2x)^3+(3x)^3+(4x)^3=33597 \\ \\ \implies 8x^3+27x^3+64x^3 = 33597 \\ \\ \implies 99x^3 = 33597 \\ \\ \implies x^3 = \frac{33597}{99} \\ \\ \implies x^3 = \frac{3733}{11}$


Now, we have to find the cubes.

Thus, we get out answer:

First Cube = $(2x)^3 = 8x^3 = 8\times \frac{3733}{11} = \frac{29864}{11}$


Second Cube = $(3x)^3 = 27x^3 = 27\times \frac{3733}{11} = \frac{100791}{11}$

Third Cube = $(4x)^3 = 64x^3 = 64\times \frac{3733}{11} = \frac{238912}{11}$


Hope it helps
Purva
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