Question

# The product of two consecutive natural numbers which are multiples of $$3$$ is equal to $$810$$. Find the two numbers.

Solution

## Let the two consecutive natural numbers which are multiples of $$3$$ be $$3x$$ and $$3(x+1)$$Now, $$3x(3x+3)=810$$$$\Rightarrow x^2+x=90$$$$\Rightarrow x^2+x-90=0$$$$\Rightarrow (x+10)(x-9)=0$$$$\Rightarrow x=9$$ or $$x=-10$$Rejecting negative value of $$x$$, because number are natural. We have $$x=9$$Hence, the required numbers are $$27$$ and $$30$$Maths

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