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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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