Question

Three numbers are in ratio 3:4:5 and the sum of their cubes is 1728000. Find the numbers.​

Answer 1

$\large\underline{\underline\mathrm\green{QUESTION}}$

Three numbers are in ratio 3:4:5 and the sum of their cubes is 1728000. Find the numbers.

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$\large\underline{\underline\mathrm\pink{SOLUTION}}$

GIVEN

• The number are in the ratio 3:4:5.
• Sum of their cubes = 1728000

TO FIND

• The Numbers.

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Let, The Numbers be 3x, 4x and 5x

ACCORDING TO QUESTION

$\bold{\implies (3x)³+(4x)³+(5x)³ = 172800}$

$\bold{\implies 27x³ + 64x³ +125x³ = 1728000}$

$\bold{\implies 216x³ =1728000}$

$\bold{\implies x³ =8000}$

$\bold{\implies x = \sqrt[3]{8000}}$

$\bold{\implies x = 20}$

THEREFORE

• 3x = 3×20 = 60
• 4x = 4×20 = 80
• 5x = 5×20 = 100