Question

Find two consecutive positive multiples of 3 whose product is 270.

Answer 1

$$\begin{gathered} \text{Let the two consecutive multiples of 3 be 3}x\text{and 3}(x+1). \\ \text{According to the question:} \\ \text{3}x\text{× 3}(x+1)=270 \\ \Rightarrow 9x(x+1)=270 \\ \Rightarrow x(x+1)=30 \\ \Rightarrow x^2+x-30=0 \\ \Rightarrow x^2+(6-5)x-30=0 \\ \Rightarrow x^2+6x-5x-30=0 \\ \Rightarrow x(x+6)-5(x+6)=0 \\ \Rightarrow (x+6)(x-5)=0 \\ \Rightarrow x+6\text{= 0 or}x-5\text{= 0} \\ \Rightarrow x=-6\text{or}x\text{= 5} \\ \mathrm{If}x=-6,\mathrm{the}\text{two consecutive multiples of 3 are {3}\times (-6)=-18\}\text{and {}3\times (-6)+3=-15\}. \\ \mathrm{If}x\text{= 5, the two consecutive multiples of 3 are {3}\times \text{5 = 15} and {3}\times \text{5 + 3 = 18}} \\ \text{Hence, the two consecutive positive multiples of 3 are}\left(\text{15, 18}\right)\text{.} \end{gathered}$$