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three numbers are in the ratio 1:2:3.The sum of their cubes is 98784. Find the numbers.

Let the no.s be x 

THEREFORE -
                                       x3 +(2x)3+(3x)3=98784

                                 => x3+23x3+33x3=98784

=>                                  x3+8x3+27x3=98784

                                 =>36x3=98784

                                x3=98784/36

                   =>  x3=2744

                  x=CUBE ROOT of 2744

THEREFORE x=14

HENCE,

FIRST NO. IS  14

Second no is 2x =28 

Third no. is 3x=42

TO CHECK THE ANS FIND THE CUBES OF THESE NO.s AND THEN ADD IT

PLS THUMPS UP!!!!!!!!!!!!!!! :)

 

 

 

 

 

 

 

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  • 7
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LET THE NUMBERS BE x , 2x ,3x  respectively 

Their ratio : 1:2:3

THEREFORE,

1x cube + 2x cube +3x cube =987884

1x cube + 8 x cube + 27 x cube

36 x cube = 98784 

x cube =98784/36

x cube = 2744

x= cube root of 2744

therefore x = 14 hence, 

first no is 14

second no.= 28

third no is 42

so you get the answer

 

 

  • 3

As the numbers are in the ratio 1:2:3, we can assume the number to be x, 2x and 3x.

Given, sum of the cubes = 98784

(x)3 + (2x)3 + (3x)3 = 98784

After simplication, the equation becomes like this : 

x3 + 8x3 + 27x3 = 98784

As there are like terms, we can add the numbers :

36x3 = 98784 

Take 36 to the other side of equation, it become :

x3 = 98784 / 36 

x3 = 2744

The cube root of 2744 is 14

x = 14

Now we have got x = 14, then :

2x = 2 * 14 = 28

3x = 3 * 14 = 42

Therefore, the numbers are 14, 28 and 42.

  • 2
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