Example 1
If x + 1/x = 8, what is the value of x² + 1/x²?
Answer: A) 62
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 8² − 2 = 62.
Algebra questions for competitive exams: rules, worked examples and practice
Algebra questions in these exams are short identity problems, such as finding x² + 1/x² from x + 1/x.
Key rules and formulas
- If x + 1/x = k, then x² + 1/x² = k² − 2.
- If x − 1/x = k, then x² + 1/x² = k² + 2.
- x³ + 1/x³ = k³ − 3k when x + 1/x = k.
- (a + b)² = a² + 2ab + b²; a³ + b³ = (a + b)(a² − ab + b²).
Common traps
- Using +2 instead of −2 (and vice versa).
- Solving for x when the identity gives the answer directly.
Where Algebra is asked
- SSC CGL Tier 1 (Quantitative Aptitude)
- SSC CGL Tier 2 (Mathematical Abilities)
Worked examples
Example 2
If x + 1/x = 9, what is the value of x² + 1/x²?
Answer: C) 79
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 9² − 2 = 79.
Example 3
If x + 1/x = 6, what is the value of x² + 1/x²?
Answer: D) 34
(x + 1/x)² = x² + 1/x² + 2, so x² + 1/x² = 6² − 2 = 34.
Frequently asked questions
What is Algebra in competitive exams?
Algebra questions in these exams are short identity problems, such as finding x² + 1/x² from x + 1/x.
Which exams ask Algebra questions?
On MockBazaar, Algebra questions appear in SSC CGL Tier 1, SSC CGL Tier 2.
What is the most common mistake in Algebra?
Using +2 instead of −2 (and vice versa).