Question

Three numbers are in a ratio 1:2:3 the sum of their cubes is 7776 find the numbers

Answer 1

Answer:

The numbers are 6,12 & 18

Answer 2

Step-by-step explanation:

SOLUTION

Let the three numbers be x, 2x and 3x.

Then,

${x}^{3} + (2x)^{3} + (3x)^{3} = 7776$

$= > {x}^{3} + {8x}^{3} + {27x}^{3} = 7776$

$= > {36x}^{3} = 7776$

$= > x^{3} = \frac{7776}{36}$

$= > {x}^{3} = 216$

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

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

$= > x = 2 \times 3$

$= > x = 6$

Therefore,

x = 6, 2x = 2×6 = 12 and 3x = 3×6 = 18.

Hence,

the three numbers are 6, 12, 18.