Algebra | SuccessSetu

🔹 Square Formula

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

a² - b² = (a+b)(a-b)

Example: (2+3)² = 4+9+12 = 25

🔹 Cube Formula

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

Example: (2+1)³ = 8+1+6 = 15

🔹 Important Identity

a³+b³ = (a+b)(a²-ab+b²)

a³-b³ = (a-b)(a²+ab+b²)

Example: 8+27 = (2+3)(4-6+9)

🔹 Power Formula

If x+1/x = k → x²+1/x² = k²-2

If x-1/x = k → x²+1/x² = k²+2

If x+1/x=5 → x²+1/x²=23

🔹 Conjugate Rule

1/(a+√b) = (a-√b)/(a²-b)

1/(5+√24)=5-√24

🔹 Componendo & Dividendo

If a/b=c/d → (a+b)/(a-b)=(c+d)/(c-d)

Used in ratio questions

📝 Practice Questions

Q1. Find (x² + 1/x²) if x+1/x = 6

Answer: 34

Q2. Find (a+b)³ if a=2, b=1

Answer: 27

Q3. Simplify: a³ - b³

Answer: (a-b)(a²+ab+b²)

Q4. Find value of (x-1/x)² if x+1/x=7

Answer: 45

🔹 Power Formula (Type 1)

If x + 1/x = k

⬇

x² + 1/x² = k² - 2

⬇

x³ + 1/x³ = k³ - 3k

Example: If x+1/x = 5
x²+1/x² = 23
x³+1/x³ = 110

🔹 Power Formula (Type 2)

If x - 1/x = k

⬇

x² + 1/x² = k² + 2

⬇

x³ - 1/x³ = k³ + 3k

Example: If x-1/x = 4
x²+1/x² = 18

🔹 Square Root Form

If x + 1/x = √t

⬇

x³ + 1/x³ = (t - 3)√t

Used in advanced problems

🔹 Same Power Formula

If x + 1/x = k

⬇

x - 1/x = √(k² - 4)

⬇

x + 1/x = √(k² + 4)

🔹 Higher Power Formula

x⁴ - 1/x⁴ = (x²+1/x²)(x+1/x)(x-1/x)

x⁵ + 1/x⁵ = (x²+1/x²)(x³+1/x³)-(x+1/x)

Used in Olympiad & SSC CGL

🔹 Important Result

If x + 1/x = √3

⬇

x³ + 1/x³ = 0