Question

Three number are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$. If the sum of their squares is $244$ find the number.

Answer 1

Let the numbers be $\frac{x}{2},\frac{x}{3},\frac{x}{4}$

$\frac{x^2}{4}+\frac{x^2}{9}+\frac{x^2}{16}=244\frac{61}{144}{x}^2=244x^2=144\times 4x=\pm 24$

So the numbers are

$x=\pm 24\pm 12,\pm 8,\pm 6$