Question

The product of Tow consecutive numbers is 306 find the numbers .

Class 10th


Quadratic equation .

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Answer 1

hey mate!

Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

Hence, numbers are x = 17 and (x +1) = 18

Answer 2

The product of two consecutive numbers is 306. Find the numbers.

Answer : 17 and 18.

Let's see the answer step by step.

Lets consider the 2 unknown numbers as (x) and (x + 1).

As per your question,

Product of x and (x + 1) is 306

(x) (x + 1) = 306

x^2 + x = 306

Taking (306) to the L.H.S,

x^2 + x - 306 = 0

Splitting the middle term,

x^2 + 18x - 17x - 306 = 0

x( x + 18 ) - 17( x + 18 ) = 0

(x - 17) (x + 18) = 0

x = 17 or x = -18

But,

Negative numbers can't be accepted.

Hence,

x = 17

x + 1 = 17 + 1 = 18

Hence,

The required numbers are 17 and 18.

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