Question

. The product of two consecutive odd numbers is 4623. Which is the greater of the two numbers’?

Answer 1

Let x = a odd number
(x+2) = its consecutive odd number.

The product of two consecutive odd numbers is 4623
x(x+2) = 4623
x² + 2x = 4623
x² + 2x - 4623 = 0
x² + 69x - 67x - 4623 = 0
x(x+69) - 67(x+69) = 0 
(x+69)(x-67) = 0
x= 67
Grater odd number = (x+2) = 67+ 2 = 69  Ans.

Answer 2

The greater of the two numbers is 69.

When taking negative odd numbers, the greator is -67.

Given:

• The product of two consecutive odd numbers is 4623.

To find:

• Which is the greater of the two numbers ?

Solution:

Concept to be used:

Assume two consecutive odd numbers,multiplication gives a quadratic equation,solution of the equation give numbers.

Step 1:

Assume the numbers.

Let x is the first odd number.

next consecutive odd number will be x+2.

Step 2:

Form the equation.

$x(x+2)=4623$

or

$\bf x^{2} +2x-4623=0$

Step 3:

Solve the quadratic equation.

$x^{2} +69x-67x-4623=0$

or

$x(x+69)-67(x+69)=0$

or

$(x+69)(x-67)=0$

or

$\bf x=67$

or

$\bf x=-69$

Case 1:

If taking x=67.

The smaller odd number is 67 and larger is 67+2=69.

Case 2:

If taking x=-69.

The smaller odd number is -69 and larger is -69+2=-67.

Thus,

The greater of two odd numbers 69 or -67.

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