There exist three numbers in the ratio of 3 : 2 : 7 such that the sum of their squares is equal to 558. The three numbers will be respectively:

9, 6, 21

The correct answer is Option (2) → 9, 6, 21

Step 1: Represent numbers

Let the numbers be:

$3x, 2x, 7x$

Step 2: Sum of squares

$(3x)^2 + (2x)^2 + (7x)^2 = 558$

$9x^2 + 4x^2 + 49x^2 = 558$

$62x^2 = 558$

$x^2 = \frac{558}{62} = 9 ⟹ x = 3$

Step 3: Find the numbers

$3x = 9, \quad 2x = 6, \quad 7x = 21$

Answer: 9, 6, 21