Question

If x=3+2×√(2, then find the value of √(x - 1/√(x

Answer 1

Solution:

x = 3+2√2 ----(1)

i ) √x = √3+2√2

= √2+1+2√2×√1

= √(√2)²+1²+2×√2×1

= √(√2+1)²

= √2 + 1 ----(2)

ii) 1/√x = 1/(√2+1)

Regionalizing the denominator, we get

= (√2-1)/[(√2+1)(√2-1)]

= (√2-1)/[(√2)²-1²]

= (√2-1)/(2-1)

= √2-1 ----(3)

Now ,

√x + 1/√x

= √2+1+√2-1

= 2√2

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