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if x=3-2√2 then find the value of √x+1/√x
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Answer:
2√2
Step-by-step explanation:
x = 3 - 2√2
√x = √( 3 - 2√2 )
⇒ √x = √( 2 - 2√2 + 1 )
⇒ √x = √( √2 - 1 )²
⇒ √x = √2 + 1
1/√x = 1/( √2 + 1 )
⇒ 1/√x = 1/(√2 + 1 ) × ( √2 - 1 )/(√2 - 1 )
⇒ 1/√x = (√2 - 1 ) / ( 2 - 1 ) = √2 - 1
Hence √x + 1/√x
⇒ √2 + 1 + √2 - 1
⇒ 2√2
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