If x = 5 + 2√6 then find the value of √x + 1/√x.
Answers
Answered by
2
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Answered by
2
Answer:
The value of √x + (1/√x) is 2√3.
Step-by-step explanation:
Given:
x = 5 + 2√6
To find:
Value of √x + (1/√x) = ?
Solution:
We have,
x = 5 + 2√6
It can be written as,
=> x = 3 + 2 + 2√6
=> x = (√3)^2 + (√2)^2 + 2 × √3 × √2
=> x = (√3 + √2)^2
=> √x = (√3 + √2)
since, 1/√x
= 1/(√3 + √2)
=> [1/(√3 + √2)]×[(√3 - √2)/(√3 - √2)]
=> [1(√3 - √2)]/[(√3 + √2)(√3 - √3)]
since,(a + b)(a - b) = a^2 - b^2
Where, a = √3 and b = √2.
=> (√3 - √2)/[(√3)^2 - (√2)^2]
=> (√3 - √2)/(3 - 2)
=> (√3 - √2)/1
=> √3 - √2
Therefore,
=> √x + (1/√x)
=> √3 + √2 + √3 - √2
=> 2√3
Hence, the value of √x + (1/√x) is 2√3.
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