Math, asked by afridali, 11 months ago

1. Three numbers are in the ratio 2 : 3:4. The sum of
their cubes is 72171. Find the numbers.

Answers

Answered by harshit18072004
10

Step-by-step explanation:

Let the numbers be 2x, 3x and 4x

then

(2x) ^3 + (3x) ^3 + (4x) ^3 = 72171

8x^3 + 27x^3 + 64x^3 = 72171

take x^3 common

then

x^3(8 + 27 + 64) = 72171

x^3(99) = 72171

x^3 = 72171/99

x^3 = 729

x = ³√729

x = 9

Numbers are

2x = 2 * 9 = 18

3x = 3 * 9 = 27

4x = 4 * 9 = 36

Hope it will be helpful


harshit18072004: mark as brainliest
harshit18072004: plaese
Answered by Anonymous
8

\mathfrak{\large{\underline{\underline{Given:-}}}}

The sum of cubes of three number is 72171.

\mathfrak{\large{\underline{\underline{To find:-}}}}

The numbers = ?

\mathfrak{\large{\underline{\underline{Solution :-}}}}

Let the given number in ratio be 2x , 3x and 4x.

According to question.

\bold{</strong><strong>{(2x)}^{3}  +  {(3x)}^{3}  +  {(4x)}^{3}  = </strong><strong>7</strong><strong>2</strong><strong>1</strong><strong>7</strong><strong>1</strong><strong> </strong><strong>}

\implies \bold{</strong><strong> </strong><strong>8 {x}^{3}  + 27 {x}^{3}  + 64 {x}^{3}  = </strong><strong>7</strong><strong>2</strong><strong>1</strong><strong>7</strong><strong>1</strong><strong>}

\implies \bold{</strong><strong>9</strong><strong>9</strong><strong>{x}^{3} </strong><strong>=</strong><strong> </strong><strong>7</strong><strong>2</strong><strong>1</strong><strong>7</strong><strong>1</strong><strong> </strong><strong> }

\implies \bold{</strong><strong>{x}^{3} </strong><strong>=</strong><strong> </strong><strong>7</strong><strong>2</strong><strong>9</strong><strong> }

\bold{</strong><strong>x</strong><strong> </strong><strong>=</strong><strong> </strong><strong>9</strong><strong> }

hence, numbers are :-

2x = 9×2 = 18

3x = 9 ×3 = 27

4x = 9 × 4 = 36

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