Question

The sum of cubes of 3 numbers which are in the ratio 1:2:3 is 7776. Find the numbers

Answer 1

Answer:

6, 12, 18

Step-by-step explanation:

Let the numbers be 1x:2x:3x.

1x^3+8x^3+27x^3=7776

36x^3=7776

x^3=7776/36

x^3=216

x=6

1x=6

2x=12

3x=18

Answer 2

Given :

• Ratio of three numbers = 1 : 2 : 3
• Sum of cubes = 7776

To find :

• The three numbers

Solution :

Let the common ratio be x .

Therefore, the three numbers are x , 2x and 3x .

A/ Q

(x)³ + (2x)³ + (3x)³ = 7776

x³ + 8x³ + 27x³ = 7776

36x³ = 7776

x³ = 7776/36

x³ = 216

$\tt x = \sqrt[3]{216}$

x = 6

So the three numbers are :

• x = 6
• 2x = 2 × 6 = 12
• 3x = 3 × 6 = 18

___________________________

The cube of any number is the number multiplied with itself three times . Hence a³ = a × a × a

When the cubes are removed , cube root is used .

Cube is given the name after the volume of the cube . Since , each side of cube is a , therefore volume becomes a³ .