Question

Question #1
Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. Find the largest number​

Answer 1

Step-by-step explanation:

let the no of 2x 3x and 4x

(2x)^3 + (3x)^3 +(4x)^3 = 33957

8x^3 + 27x^3 + 64^3 = 33957

99x^3 = 33957

x = 33957/99 = 343

x^3 = 7× 7× 7 (Resolving 343 into prime factor)

x=

$\sqrt[3]{7 \times7 \times 7}$

= 7

hence the numbers are

2x = 2×7= 14,3x = 3×7 = 21

and 4x= 4×7= 28

the largest no will be 28

hope it help you

Answer 2

Question:

Three numbers are in the ratio 2:3:4. The sum of their cubes is 33957. Find the largest number

To find:

• Largest number

Given:

• Three numbers are in the ratio of 2:3:4.

• Sum of their cubes = 3395

Let:

• 1 number = 2x

• 2 number = 3x

• 3 number = 4x

Solution:

As it is told:-

Sum of cubes of these three numbers = 3395

• .°. (2x)³ + (3x)³ + (4x)³ = 33957

• → 8x³ + 27x³ + 64x³ = 33957

• →35x³ + 64x³ = 33957

• →99x³ = 33957

• →x³ = 33957/99

• →x³ = 343

• →x = ³√(343)

• →x= ³√(7 ×7 ×7 )

• → x=7

Verification:

• → (2x)³ + (3x)³ + (4x)³ = 33957

• →(2 × 7)³ + (3 × 7)³ + (4 × 7)³ = 33957

• →(14)³ + (21)³ + (28)³ = 33957

• → (14 × 14 × 14) + (21 ×21 ×21) + (28 × 28 × 28) = 33975

• →2744 + 9261 + 21952 = 33975

• →33957 = 33957

LHS = RHS

Hence verified!

Now we know 4x is larger than 3x and 2x

.°. 4x is largest number

• → Largest number = 4x

• → Largest number = 4 × 7

• → Largest number = 28

Happy learning! :)