Question

a=√2+1 find the value of(a-1/a)2​

Answer 1

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Answer 2

GIVEn

a=√2+1 find the value of(a-1/a)²

SOLUTIOn

• a = √2 + 1

→ 1/a = 1/√2 + 1

Rationalize its denominator

→ 1/a = 1/√2 + 1 × √2 - 1/√2 - 1

→ 1/a = √2 - 1/(√2)² - (1)²

→ 1/a = √2 - 1/2 - 1

→ 1/a = √2 - 1

Value of (a - 1/a)²

→ (a - 1/a)²

Apply identities :

(a - b)² = a² + b² - 2ab

(a + b)² = a² + b² + 2ab

a² - b² = (a + b)(a - b)

→ (√2 + 1)² + (√2 - 1)² - 2 × (√2 + 1) × (√2 - 1)

→ [(√2)² + (1)² + 2*√2*1] + [(√2)² + (1)² - 2*√2*1] - 2[(√2)² - (1)²]

→ [2 + 1 + 2√2] + [2 + 1 - 2√2] - 2[2 - 1]

→ 3 + 2√2 + 3 - 2√2 - 2

→ 6 - 2 = 4