Identities | Maths

• (a + b)²= a² + 2ab + b²
• (a - b)²= a²- 2ab + b²
• a² - b² = (a - b) (a + b)
• (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)

Questions

1.( √3 + 1) ( √3 – 1)  എത്ര? 
(LD Clerk SR for ST only 2020)
Here use identity a² - b²  = (√3)² - 1² = 2

2018
1. 3.12 × 3.12 + 6.24 × 6.88 + 6.88 × 6.88

(Caretaker Male 2018)

Answer : 10²

Here use identity (3.12+6.88)²

2. x + 1/x = 5 ആയാൽ x² + 1/x² എത്ര? 
(Security Guard- Government Secretariat 2018)

(x + 1/x)2 = x² + 1/x² + 2

25 = x² + 1/x² +2

x² + 1/x² = 23

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