Question

8. IF x = 7+10^1/2 find the value ofx^1/2+1/x^1/2

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Answer 1

||✪✪ CORRECT QUESTION ✪✪||

if x = (7 + 2√10), Find the value of √x + (1/√x)..

|| ✰✰ ANSWER ✰✰ ||

→ x = 7 + 2√10

→ x = ( 5 + 2 + 2 * √5 * √2)

Comparing RHS with a² + b² + 2ab = (a+b)² , we get,

→ x = [ (√5)² + (√2)² + 2 * √5 * √2 ]

→ x = [ √5 + √2 ]²

Square - Root both sides now,

→ √x = (√5 + √2) ----------- Equation (1)

So,

(1/√x) = 1/(√5 + √2)

Rationalizing it,

→ (1/√x) = 1/(√5 + √2) * [ (√5 - √2) / (√5 - √2) ]

→ (1/√x) = [ (√5 - √2) / (5 - 2) ]

→ (1/√x) = (√5 - √2) /3 ---------- Equation (2) ,

So, putting value of Equation (1) and Equation (2) now, we get,

→ √x + (1/√x) = (√5 + √2) + {(√5 - √2) /3}

→ √x + (1/√x) = [ ( 3√5 + 3√2 + √5 - √2) / 3 ]

→ √x + (1/√x) = [ (4√5 + 2√2) /3 ]

→ √x + (1/√x) = 2(2√5 + √2)/3 . (Ans).