If $ 2500x = (455)^2 - (445)^2 $, then the value of $ x $ is: | Mathematics MCQ | Examoogle

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If $2500x = (455)^2 - (445)^2$ , then the value of $x$ is:

3.6

4.2

4.8

5.4

Correct Answer

📐 MA • Math Difference of SquaresMathematicsAlgebra

Option A

Quick Summary:

Observe that the difference $(455 - 445)$ is 10, so the expression simplifies to $10 \times (455 + 445) = 10 \times 900 = 9000$ . Dividing $9000$ by $2500$ is equivalent to $90 / 25$ , which is $3.6$ .

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📐MAMath SolutionDifference of Squares

📋 Given

An algebraic equation 2500x = $(455)^2$ - $(445)^2$ is provided.

🔢 Formula Used

a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b)a2−b2=(a−b)(a+b)

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Many students attempt to calculate the squares $455^2$ and $445^2$ individually, which is time-consuming and prone to arithmetic errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the Algebraic Identity

The right-hand side of the equation is in the form of $a^2 - b^2$ , which can be factored using the identity $a^2 - b^2 = (a - b)(a + b)$ .

4552−4452=(455−445)(455+445)455^2 - 445^2 = (455 - 445)(455 + 445)4552−4452=(455−445)(455+445)

Simplify the Terms

Calculate the difference and the sum of the terms inside the parentheses.

(10)(900)=9000(10)(900) = 9000(10)(900)=9000

Solve for x

Substitute the simplified value back into the original equation $2500x = 9000$ and solve for $x$ .

x=90002500=9025=3.6x = \frac{9000}{2500} = \frac{90}{25} = 3.6x=25009000​=2590​=3.6

✅

A is correct because the calculation of the difference of squares yields $9000$ , and dividing by $2500$ results in $3.6$ .

Core Concepts Used

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Algebraic Identities Difference of Squares Arithmetic Simplification

💡 EXAM TIP

Recognizing the difference of squares pattern is highly useful in simplification-based aptitude questions and quadratic equation solving in higher-level competitive exams.

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