Question

(2)
(or)
Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the
numbers.​

Answer 1

Answer:

$x=14\\2x=28\\3x=42$

Step-by-step explanation:

$x^{3} +(2x)^{3} +(3x)^{3}=98784$

$x^{3} +8x^{3} +27x^{3}$$= 98784$

$36x^{3} =98784$

$x^{3} =\frac{98784}{36}$

$x^{3}= 2274$

$x=\sqrt[3]{2274}$

$x=14$

$2x=14$×$2=28$

$3x=14$×$3=42$

Answer 2

$\huge{\mathbb{\fbox{\red{Answer}}}}$

let the three numbers be 1x,2x&3x.

According to given condition:

1x³+2x³+3x³= 98784

=>6x³=98784

=>x³=98784/6

=>x³= 16464

=>x= ³√16464

x=>28√21

2x= 2(28√21)=>56√42.

3x=3(28√21)=>84√63.

Hence, the three numbers are 28√21,56√42,84√63.

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