Question

three numbers are in the ratio 1 : 3 : 4 sum of their cubes is 47,104 find the numbers


please answer it please in explanation detail​

Answer 1

Step-by-step explanation:

Let the numbers x,3x,4x

Sum of their cubes=47104

${x}^{3} + {3x }^{3} + {4}^{3} = 47104 \\ {8x}^{3} = 47104 \\ {x}^{3} = \frac{47104}{8 } \\ {x}^{3 } = 5888 \\ x = \sqrt[3]{5888 = }$

Answer 2

Answer:

Three numbers are :-

8, 24 and 32

Explanation:

Given :

Three numbers are in the ratio 1 : 3 : 4 and sum of their cubes is 47104.

To Find :

All the three numbers

Solution :

Let the number be 1x, 3x and 4x.

Sum of the three cubes => 47104

$\implies \sf{}(1x)^3+(3x)^3+(4x)^3= 47104$

$\implies \sf{}1x^3+27x^3+64x^3= 47104$

$\implies \sf{}92x^3= 47104$

Divide both sides by 92

$\implies \sf{}\dfrac{92x^3}{92}=\dfrac{47104}{92}$

Cancel both 92 of left side

$\implies \sf{}x^3 =\dfrac{47104}{92}$

Let’s solve 47104/92

$\sf{}\implies x^3=\dfrac{23552}{46}$

$\sf{}\implies x^3=\dfrac{11776}{23}$

$\sf{}\implies x^3=512$

Take cube root.

$\sf{}\implies x=\sqrt[3]{512}$

$\sf{}\implies x=(512)^{\frac{1}{3}}$

$\boxed{\sf{}x=8}$

We know x = 8,therefore replace the value of x as 8

$\sf{}1\times (8)= 8$

$\sf{}3 \times (8)=24$

$\sf{}4 \times (8)=32$

Hence,numbers are 8, 24 and 32