Question

Two numbers are in the ratio 2 ratio 3. The difference of their cubes is 9,728. Find the numbers.​

Answer 1

Step-by-step explanation:

Let the numbers be 2x and 3x

According to question,

${(3x)}^{3} - {(2x)}^{3} = 9728$

$27 {x}^{3} - 8 {x}^{3} = 9728$

$19 {x}^{3} = 9728$

${x}^{3} = \frac{9728}{19}$

${x}^{3} = 512$

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

$x = 8$

Numbers =

2x = 2 × 8 = 16

3x = 3 × 8 = 24

Answer 2

☯GIVEN :

• Two numbers are in the ratio 2:3.

• Difference of their cubes = 9728

☯ TO FIND :

• Required numbers .

➲SOLUTION :

Let the required numbers are 2x and 3x.

• Difference of their cubes = 9728

$\implies \sf{ (Second \: Number)^3 - (First \:Number)^3 =9728 }$

$\implies \sf{(3x)^3 -(2x)^3 = 9728 }$

$\implies \sf{27x^3 -8x^3 = 9728}$

$\implies \sf{19x^3 = 9728}$

$\implies \sf{x^3 = \cancel {\dfrac{9728}{19}}}$

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

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

$\implies\sf{x = \sqrt[ 3]{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2} }$

$\implies \sf{x = \sqrt[ 3]{2^3 \times 2^3 \times 2^3} }$

$\implies\sf{x = 2 \times 2 \times 2}$

$\implies\underline { \huge{ \boxed{\bf{x = 8}}}}$

$\huge { \pink{\therefore}}$First Number = $\bf {2 \times 8 = 16}$

$\huge { \red{\therefore}}$ Second Number = $\bf {3 \times 8 = 24}$