If x=3+2√2 then,find the value of x to the power 1/2 + x to the power 1/2
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Answer:
√x + 1/√x = 2√2
Solution:
- Given : x = 3 + 2√2
- To find : √x + 1/√x = ?
We have ;
=> x = 3 + 2√2
=> x = 2 + 1 + 2√2
=> x = 2 + 2√2 + 1
=> x = (√2)² + 2•√2•1 + 1²
=> x = (√2 + 1)²
=> √x = √2 + 1
Now,
If √x = √2 + 1
Thus,
=> 1/√x = 1/(√2 + 1)
=> 1/√x = (√2 - 1)/(√2 + 1)(√2 - 1)
=> 1/√x = (√2 - 1)/[(√2)² - 1²]
=> 1/√x = (√2 - 1)/(2 - 1)
=> 1/√x = (√2 - 1)/1
=> 1/√x = √2 - 1
Now,
=> √x + 1/√x = (√2 + 1) + (√2 - 1)
=> √x + 1/√x = √2 + 1 + √2 - 1
=> √x + 1/√x = 2√2
Hence,
Required answer is ; 2√2
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