Algebra & Polynomial Identities
Practice 490+ official SSC CGL & CHSL Algebra PYQs online. Master x + 1/x = k shortcuts, symmetric polynomials, timed drills & step-by-step solutions.
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Algebra & Polynomial Identities:
- Reciprocal Identities: x + 1/x = k => x² + 1/x² = k² - 2
- Cubic Identities: x³ + 1/x³ = k³ - 3k
- Symmetric Identity: a³ + b³ + c³ - 3abc = (a+b+c)(a²+b²+c²-ab-bc-ca)
- Special Condition: If a + b + c = 0, then a³ + b³ + c³ = 3abc
- Quadratic Equations & Roots Value Putting Techniques
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Algebra questions in under 45 seconds:
If x + 1/x = 2, then x = 1 (and xⁿ + 1/xⁿ = 2 for any n).
If x + 1/x = √3, then x⁶ = -1 and x¹² = 1.
If a + b + c = 0, then a³ + b³ + c³ = 3abc directly.
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 42
- Step 1: If we assume that the num- ber of members in team A is x and number of members in team B be y.
- Step 2: Now when 3 people are shifted from team A to B, we can express it as yx yx yx x y = ⇒ 33 3/39 33/12 12 3 i When 2 people are shifted from team B to A, we can express it as ⇒− =+ () ⇒− =+ ⇒ + ⇒ + + yx yx yx y y 22 2/22 42 6
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 6
- Step 1: Understand problem conditions and equations.
- Step 2: If we assume the unit’s digit be x and ten’s digit be y Original Number =10y + x After reversing the digits Number= 10x + y When the second number increases by 18, ∴+ ( ) −+( ) = ⇒− = ⇒− = 10/10 18/99 18 2 xy yx xy xy Numbers formed by reversing the digits and always increases the actual number by 18 should fulfil, the above equation condition. x y
- Step 3: Evaluating gives verified answer: 6.
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 10/27
- Step 1: Understand problem conditions and equations.
- Step 2: 3x2 + 5x + 3 = 0 ⇒ + = − ⇒+ =− ⇒+ =− ∴+ =− 33 5 3 3 5 1 5/15 3 2x x x x x x xx x x x ⇒+ =+ ++ ⇒+ −+ x x x x x x x x x x x x 11 3/11 1 3 1 3 3 3 3 = ⇒+ =− −− = − += −+ = x x x x 3 3 3 3 1/15 3 3 5 3/125 27 5/125 136/27 10 0/27
- Step 3: Evaluating gives verified answer: 10/27.
⚡ Speed Tip: Verify intermediate calculations and units.
❓ Frequently Asked Questions (FAQs)
How to solve x + 1/x = k problems in 5 seconds in SSC CGL?
Remember: x² + 1/x² = k² - 2, and x³ + 1/x³ = k³ - 3k. Plug k directly.