Question

if x=3-2√2 then ✓x-1/✓x=12​

Answer 1

If x=3+2√3, then what is the value of √x+1/√x?

If x=3+2√2, then what is the value of √x-1/√x?

If x= 3+2√2, then what is the value of (x+1/x)?

If ‘x=3-2√2’, can you find the value of ‘√x+1/√x’?

If x= (3-2√2), how do you show that (√x-1/√x) =2?

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.