Question

If a = √2 +1, then find the value of a – 1/a.​

Answer 1

Answer:

The value of a - 1/a is 2.

Step-by-step explanation:

Given,

• a = √2 + 1

To Find,

• The value of a - 1/a.

Solution,

a = √2 + 1

→ 1/a = 1/(√2 + 1)

→ 1/a = 1/(√2 + 1) × (√2 - 1)/(√2 - 1)

→ 1/a = (√2 - 1)/[(√2 + 1)(√2 - 1)]

[(a + b)(a - b) = a² - b²]

→ 1/a = (√2 - 1)/[(√2)² - 1²]

→ 1/a = (√2 - 1)/(2 - 1)

→ 1/a = (√2 - 1)/1

→ 1/a = √2 - 1

a - 1/a = a - 1/a

→ a - 1/a = √2 + 1 - (√2 - 1)

→ a - 1/a = √2 + 1 - √2 + 1

→ a - 1/a = 2

Required Answer,

The value of a - 1/a is 2.

Answer 2

a=

$(\sqrt{2} + 1)$