Question

Find two consecutive multiples of 3 whose product is 648.

Answer 1

Let the required consecutive multiples of 3 be 3x and 3(x + 1).

According to the given condition, 

3x × 3(x + 1) = 648 

⇒ 9(x² + x) = 648 

⇒ x² + x = 72

⇒ x² + x – 72 = 0 

⇒ x² + 9x – 8x – 72 = 0 

⇒ x(x + 9) – 8(x + 9) = 0 

⇒ (x + 9)(x – 8) = 0 

⇒ x + 9 = 0 or x – 8 = 0 

⇒ x = –9 or x = 8 

∴ x = 8   ...(Neglecting the negative value) 

When x = 8, 

3x = 3 × 8

= 24 

3(x + 1) = 3 × (8 + 1)

= 3 × 9

= 27 

Hence, the required multiples are 24 and 27.