Question

Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

Answer 1

Suppose the numbers = 2z, 3z, 4z
Given, the sum of their cubes = 0.334125
As per question,
$(2z{)}^3+(3z{)}^3+(4z{)}^3=0.334125$
or $8z^3+27z^3+64z^3=0.334125$
or $99z^3=0.334125$
or $z^3=0.334125÷99$
$x^3=\frac{0.334125}{99}=0.003375$
$x^3=\frac{3375}{1000000}$
$x=\sqrt[3]{3\frac{15\times 15\times 15}{10\times 10\times 10\times 10\times 10\times 10}}=\frac{15}{10\times 10\times 10}=0.015$
Hence, the required numbers are
$2\times 0.015=0.03$
$3\times 0.015=0.045$
$4\times 0.015=0.06$