Question

If x= 3+2√2 then find x+1\x
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Answer 1

Required Answer:-

Given:

• x = 3 + 2√2

To Find:

• The value of (x + 1/x).

Concept Used:

• Rationalization.

Solution:

Given that,

→ x = 3 + 2√2

→ 1/x = 1/(3 + 2√2)

→ 1/x = 1/(3 + 2√2) × (3 - 2√2)/(3 - 2√2)

→ 1/x = (3 - 2√2)/[(3)² - (2√2)²]

→ 1/x = (3 - 2√2)/(9 - 8)

→ 1/x = (3 - 2√2)

Therefore,

→ x + 1/x = 3 + 2√2 + 3 - 2√2

→ x + 1/x = 6

→ Therefore, the value of (x + 1/x) is 6.

Answer:

• (x + 1/x) = 6.