Question

Find two consecutive multiples of 3 whose product is 270.

Answer 1

Let the two consecutive multiples of 3 be $$x$$ and $$(x + 3)$$.

According to the problem: $$x(x + 3) = 270$$

$$x^2 + 3x - 270 = 0$$ 

Factoring the quadratic equation: $$x^2 + 18x - 15x - 270 = 0$$

$$x(x + 18) - 15(x + 18) = 0$$

$$(x + 18)(x - 15) = 0$$

$$x = -18 \quad \text{or} \quad x = 15$$ 

Taking the positive solution $$x = 15$$:

The next consecutive multiple of 3 is $$15 + 3 = 18$$.

If negative multiples are considered, $$x = -18$$ gives $$-18$$ and $$-15$$.

Hence, the required consecutive multiples of 3 are 15 and 18 (or $$-18$$ and $$-15$$).