Question

1 \√5+√2. simplify
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Answer 1

Step-by-step explanation:

Given

Simplify 1/(√5 + 2)

Solution

→ 1/(√5 + 2)

★ Rationalise its denominator

→ 1/(√5 + 2) × (√5 - 2)/(√5 - 2)

→ (√5 - 2)/(√5)² - (2)²

Apply identity :

a² - b² = (a + b)(a - b)

→ (√5 - 2)/5 - 4

→ √5 - 2

Extra Information

(a + b)² = a² + b² + 2ab

(a - b)² = a² - b² - 2ab

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)