Mathematics

Two consecutive natural numbers each of which is multiple of 3 and with their product = 108.
Statement 1: The required natural numbers are 9 and 12.
Statement 2: If two natural numbers are 3x and 3x + 3; 3x(3x + 3) = 108.
Both the statement are true.
Both the statement are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.

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Both the statement are true.

Reason

Let the two consecutive natural numbers each of which is multiple of 3 be 3x and 3(x + 1).

Product = 108

⇒ 3x $\times$ 3(x + 1) = 108

⇒ 3x $\times$ (3x + 3) = 108

⇒ 9x² + 9x = 108

⇒ 9x² + 9x - 108 = 0

⇒ 9(x² + x - 12) = 0

⇒ x² + x - 12 = 0

⇒ x² + 4x - 3x - 12 = 0

⇒ x(x + 4) - 3(x + 4) = 0

⇒ (x + 4)(x - 3) = 0

⇒ (x + 4) = 0 or (x - 3) = 0

⇒ x = -4 or x = 3

Since, number are two natural numbers. So, x = 3.

And, when x = 3, two consecutive numbers = 3 x 3 = 9 and 3 x (3 + 1) = 3 x 4 = 12

So, both statements are true.

Hence, option 1 is the correct option.

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