Question

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

Answer 1

Answer:

Let the two consecutive natural numbers which are multiples of 3 be 3x and 3(x+1)

Now, 3x(3x+3)=810

⇒x

2

+x=90

⇒x

2

+x−90=0

⇒(x+10)(x−9)=0

⇒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

Step-by-step explanation:

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Answer 2

❍ Let the smaller natural number which is a multiple of 3 be x, then the other consecutive natural number which is a multiple of 3 is x + 3.

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★ According to given, x(x + 3) = 810

➻ x² + 3x - 810 = 0

➻ (x - 27) (x + 30) = 0

➻ x - 27 = 0 or x + 30 = 0

➻ x = 27 or x = -30

❐ But x is a natural number, so we reject x = -30.

∴ x = 27.

❖ Therefore,

• Hence, the numbers are 27 and 27 + 3 i.e., 27 and 30.

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