If x + 1/x = 5, find the value of x² + 1/x².

Step 1: Use the identity (x + 1/x)² = x² + 2 + 1/x². Step 2: Substitute x + 1/x = 5: (5)² = x² + 2 + 1/x². Step 3: 25 = x² + 2 + 1/x². Step 4: x² + 1/x² = 25 - 2 = 23. Therefore, the answer is 23.

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IBPS PO Algebraic Identities

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Concept Notes

Algebraic Identities— Rules & Concept

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Core Concept

Read this first — the foundation of the topic

💡Key Rules and Properties

Algebraic identities are universally true for all values of variables. They help expand, factorize, and simplify expressions. The most important ones follow specific patterns that SSC loves to test

🔑Essential Formulas

• (a + b)² = a² + 2ab + b² • (a - b)² = a² - 2ab + b² • (a + b)(a - b) = a² - b² • (a + b)³ = a³ + 3a²b + 3ab² + b³ • (a - b)³ = a³ - 3a²b + 3ab² - b³ • a³ + b³ = (a + b)(a² - ab + b²) • a³ - b³ = (a - b)(a² + ab + b²) • (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

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Exam Patterns

What examiners ask — read before attempting PYQs

SSC CGL typically asks direct substitution problems, value finding questions, and simplification using identities. Common question types include finding the value of expressions like x² + 1/x² when x + 1/x is given, or simplifying complex algebraic fractions. Shortcut Trick - The 'Recognition Method': Instead of expanding everything, learn to recognize patterns. If you see (something)² - (something else)², immediately think a² - b² = (a+b)(a-b). This saves 2-3 minutes per question.

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Worked Example

Solve this step-by-step before moving on

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Step 1

Start with the given condition x + 1/x = 5

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Step 2

Square both sides: (x + 1/x)² = 5² = 25

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Step 3

Apply the identity (a + b)² = a² + 2ab + b² Here, a = x and b = 1/x

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Step 4

(x + 1/x)² = x² + 2(x)(1/x) + (1/x)²

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Step 5

25 = x² + 2(1) + 1/x²

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Step 6

25 = x² + 2 + 1/x²

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Step 7

x² + 1/x² = 25 - 2 = 23 Therefore, x² + 1/x² = 23. Common Mistake: Students often forget the middle term in expansions. In (a + b)², many write a² + b² and miss the 2ab term. Always count terms: square of binomial has THREE terms, cube has FOUR terms. Also, students confuse signs in (a - b) expansions. Remember: alternate signs in (a - b)³.

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IBPS PO Algebraic Identities

Algebraic Identities— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Algebraic Identities — Practice Questions

60-Second Revision — Algebraic Identities