Question

If a=5-2root6 then find the value of root a minus 1/root a

Answer 1

Question:

If a = 5 - 2√6 then find the value of √a - 1/√a .

Answer:

– 2√2

Solution:

Given: a = 5 - 2√6

Thus,

=> a = 5 - 2√6

=> a = 3 + 2 - 2√6

=> a = 3 - 2√6 + 2

=> a = (√3)² - 2•√3•√2 + (√2)²

=> a = (√3 - √2)²

=> √a = √[(√3 - √2)²]

=> √a = √3 - √2

Now,

=> 1/√a = 1/(√3 - √2)

{ Rationalizing the denominator in RHS }

=> 1/√a = (√3+√2)/(√3-√2)(√3+√2)

=> 1/√a = (√3+√2)/{(√3)² - (√2)²}

=> 1/√a = (√3 + √2)/(3 - 2)

=> 1/√a = √3 + √2

Thus,

=> √a - 1/√a = (√3 - √2) - (√3 + √2)

=> √a - 1/√a = √3 - √2 - √3 - √2

=> √a - 1/√a = - 2√2

Hence,

The required value of √a – 1/√a = –2√2