Question

If x=3+2√2 then find (√x-1/√x)
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Answer 1

Step-by-step explanation:

Let √x - 1/√x = a

Squaring both the sides,

x + 1/x - 2 = a^2

Putting the value,

3–2√2 + 1/(3–2√2) - 2 = a^2

a^2 = 1 - 2√2 + 1/(3–2√2)

= [(3–2√2) (1–2√2) + 1] / 3–2√2

= {3 - 8√2 + 9} / 3–2√2

= [12 - 8√2] / 3–2√2

Rationalising both the sides

= {(12 - 8√2)(3+2√2)} ÷ (9–8)

= 36 + 24√2 - 24√2 + 16(2)

= 36 - 32

=> 4

a^2 = 4

a = √4

a = 2, -2

So,

√x - 1/√x = a = 2, -2.

Answer 2

x= 3+2√2

1/x= 1/(3+2√2)

1/x= 1/(3+2√2) ×(3-2√2)/(3-2√2)

1/x= (3-2√2)/(9-8)

1/x= 3-2√2.

Now,

x+1/x= (3+2√2)+(3-2√2)

or, x+1/x= 6

or, (√x)² + (1/√x)² = 6

or, (√x)²+(1/√x)²-2= 6-2

or, (√x - 1/√x)²= 4

or, (√x-1/√x)= √4

or, (√x - 1/√x) = 2, -2.