Math Problem Statement

The product of two consecutive odd natural numbers is 323323. Find the largest number among them.

Solution

Let the two consecutive odd natural numbers be nn and n+2n+2.

Step 1: Form the equation

The product of the two numbers is given by: n×(n+2)=323323n \times (n + 2) = 323323

Expanding this equation: n2+2n=323323n^2 + 2n = 323323

Step 2: Rearrange the equation

Rewrite it as: n2+2n323323=0n^2 + 2n - 323323 = 0

Step 3: Solve the quadratic equation

We solve the quadratic equation n2+2n323323=0n^2 + 2n - 323323 = 0 using the quadratic formula: n=b±b24ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} where a=1a = 1, b=2b = 2, and c=323323c = -323323.

Step 4: Calculate the discriminant

The discriminant is: [ b

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Equations

Formulas

n × (n + 2) = 323323
Quadratic equation formula: n^2 + 2n - 323323 = 0
Quadratic formula: n = (-b ± √(b² - 4ac)) / 2a

Theorems

Quadratic formula

Suitable Grade Level

Grades 9-12