Question

find 3 positive numbers in ratio 2 ratio 3 ratio 5 the sum of whose squares is 950

Answer 1

lets assume the numbers are 2x 3x and 5x
then as per question,

2x^2+3x^2+5x^2=950
or,10x^2=950
or,x^2=95
or,x=
$\sqrt{95}$
now the numbers are
$2 \sqrt{95}$
$3 \sqrt{95}$
and
$5 \sqrt{95}$

Answer 2

Given that 3 positives numbers are in the ratio 2 : 3 : 5

Let the numbers be 2x, 3x and 5x

Sum of the 3 numbers = 250

We can represent this info in the form (2x)² + (3x)² + (5x)² = 950

⇒ 4x² + 9x² + 25 x² = 950

⇒ 38x² = 950

⇒ x² = 950/38 = 25

⇒ x² = 25

⇒ x = 5

⇒2x = 10, 3x =15, 5x = 25

∴There for the three numbers are 10, 15 and 25.

So the three numbers are 190, 285, 475.