Question

MARKS QUESTIONS
Three numbers are in the ratio of 2:3:4. The sum of their cubes is 2673. Find the numbers.
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Answer 1

Step-by-step explanation:

let the three no.s are 2x,3x,4x

(2x)^3+(3x)^3+(4x)^3=2673

8x+27x+64x=2673

99x=2673

x=3√2673

Answer 2

The numbers are 6 , 9 and 12

Step-by-step explanation:

The ratio of the three numbers are 2:3:4

Let the numbers are 2x , 3x and 4x.

According to the question:

⇒ (2x)³ + (3x)³+ (4x)³ = 2673

⇒ 8x³ + 27x³ + 64x³ = 2673

⇒ 99x³ = 2673

⇒ x³ = 2673 / 99

⇒ x³ = 27

⇒ $x \: = \sqrt[3]{27}$

⇒ x = 3

Therefore,

★ The numbers are :

• 2x = 2 ( 3 )

⇒ 2 × 3

⇒ 6

• 3x = 3 ( 3 )

⇒ 3 × 3

⇒ 9

• 4x = 4 ( 3 )

⇒ 4 × 3

⇒ 12

★ Verification:

⇒ 6³ = 216

⇒ 9³ = 729

⇒ 12³ = 1728

• 216 + 729 + 1728 = 2673