Question

1 added to the product of two consecutive odd numbers givrn 576. What are the number

Answer 1

Answer:

The required two numbers can be either -23 and -25 or 23 and 25

Step-by-step explanation:

Given :

1 added to the product of two consecutive odd numbers gives 576.

To find :

the numbers

Solution :

Let the two consecutive odd numbers be (2x + 1) and (2x + 3)

First, let's find the product of the two numbers.

⇒ (2x + 1) (2x + 3)

⇒ 2x(2x + 3) + 1(2x + 3)

⇒ 4x² + 6x + 2x + 3

⇒ 4x² + 8x + 3

Now, 1 added to the product gives 576.

⇒ 4x² + 8x + 3 + 1 = 576

⇒ 4x² + 8x + 4 = 576

⇒ 4x² + 8x = 576 - 4

⇒ 4x² + 8x - 572 = 0

⇒ 4(x² + 2x - 143) = 0

⇒ x² + 2x - 143 = 0

Solving the quadratic equation,

⇒ x² + 13x - 11x - 143 = 0

⇒ x(x + 13) - 11(x + 13) = 0

⇒ (x + 13) (x - 11) = 0

⇒ x + 13 = 0 ; x = -13

⇒ x - 11 = 0 ; x = +11

If x = -13,

2x + 1 = 2(-13) + 1 = -26 + 1 = -25

2x + 3 = 2(-13) + 3 = -23

⇒ The two numbers are -25 and -23

If x = +11,

2x + 1 = 2(11) + 1 = 23

2x + 3 = 2(11) + 3 = 25

⇒ The two numbers are 23 and 25