Question

Three numbers are to one another as 2:3:4.If the sum of their cubes is 50688,find the numbers.​

Answer 1

Answer:

That is the answer, tell me if it helps the answer is in the pic

Answer 2

Given:-

• Ratio of three numbers = 2 : 3 : 4
• Sum of their cubes = 50688

To find:-

• The numbers

Answer:-

As the ratio of the numbers is 2 : 3 : 4,

let the numbers be 2x, 3x and 4x.

▪Cube of first number = (2x)³

▪Cube of second number = (3x)³

▪Cube of third number = (4x)³

According to the question, the sum of these cubes is 50688.

So,

(2x)³ + (3x)³ + (4x)³ = 50688

→ 8x³ + 27x³ + 64x³ = 50688

→ 99x³ = 50688

→ x³ = 50688/99

→ x³ = 512

→ x = 8

Hence, the numbers are:-

• 2x = (2 × 8) = 16 Ans.
• 3x = (3 × 8) = 24 Ans.
• 4x = (4 × 8) = 32 Ans.

Verification:-

Given equation: (2x)³ + (3x)³ + (4x)³ = 50688

L.H.S.:-

(2x)³ + (3x)³ + (4x)³

Putting x = 8,

→ 16³ + 24³ + 32³

→ 4096 + 13824 + 32768

→ 50688

R.H.S.:-

50688

L.H.S. = R.H.S.

Hence verified.