Question

the product of four consecutive natural numbers is 840 find the numbers (with a quadratic equation)​

Answer 1

Answer:

The 4 consecutive numbers are 4, 5, 6, 7.

Step-by-step explanation:

Let the first number be x

Then, the second will be x + 1

The third will be x + 2

The forth will be x +3

Now, According to the question the sum of the 4 consecutive number is 840.

So,

x × (x + 1) × (x + 2) × (x + 3) = 840

⇒ [(x² + 3x + 1) −1) × (x² + 3x + 1) +1] = 840

⇒ (x² + 3x + 1)² −1 = 840

⇒ (x² + 3x + 1)² = 841

⇒ (x² + 3x + 1)² = 29²

⇒ (x² + 3x + 1) = 29

⇒ x² + 3x + 1 –29 = 0

⇒ x² + 3x - 28 = 0

⇒ (x + 7) (x - 4) = 0

⇒ x = -7 and x = 4

Taking x as -7 is not possible because -7 does not belongs to the natural number.

∴ x = 4

Now, taking value of x as 4 we get :

x = 4 ; x + 1 = 5 ; x + 2 = 6 ; x + 3 = 7

∴ The 4 consecutive numbers are 4, 5, 6, 7.

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