Question

if x=3+2√2 then find the value of (x-1/x) ^3​

Answer 1

Answer:

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.