Question

The Sum of three Consecutive multiples of 7 is 588. What are the numbers

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Answer 1

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Multiples of 7 are 7, 14, 21, 28...

Here the difference between two consecutive multiples will be 7

In general, the difference between two consecutive multiples of n will be n

Let two consecutive numbers be x and x+7

Given that sum of the squares of two consecutive multiples is 637

⇒x² +(x+7)²=637

⇒ x² +x² +14x+49=637

⇒ 2x²+14x+49−637=0

⇒ 2x² +14x−588=0

⇒ 2(x²+7x−294)=0

⇒ x²+7x−294=0

⇒ x²+21x−14x−294=0

⇒ x(x+21)−14(x+21)=0

⇒ (x+21)(x−14)=0

⇒ x+21=0 or x−14=0

⇒ x=−21 or x=14

Case(1)

If one number is 14

Other, number =x+7=14+7=21

So The product of two multiple 14×21=294

Case(2)

If one number is −21

Other, number =x+7=−21+7=−14

So The product of two multiple −14×−21=294

In both the cases, the answer is 294.