Question

1. If x=1/(3+2V2), then the value of x-1/x​

Answer 1

Let √x - 1/√x = aSquaring both the sides,x + 1/x - 2 = a^2Putting the value,3–2√2 + 1/(3–2√2) - 2 = a^2a^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√2Rationalising both the sides= {(12 - 8√2)(3+2√2)} ÷ (9–8)= 36 + 24√2 - 24√2 + 16(2)= 36 - 32=> 4a^2 = 4a = √4a = 2, -2So,√x - 1/√x = a = 2, -2.