Question

if x+1/x=3+2√2 then √x-1/√x​

Answer 1

The value would be√( 1+2√2)

1) First find the square of the desired term

(√x-1/√x)² =x+1/x -2*x*1/x

(√x-1/√x)²= x+1/x -2

2) Substituting the value of x+1/x in the equation

(√x-1/√x)² = 3+2√2 - 2

(√x-1/√x)² = 2+1+2√2-2

(√x-1/√x)² =(√2)² +1²+2*1*√2-2

3) Using identity of (a+b)²

(√x-1/√x)² = (√2+1)²- 2

(√x-1/√x)² = (√2+1)²-(√2)²

4) Using identity of a²-b²

(√x-1/√x)² =(√2+1-√2)(√2+1+√2)

(√x-1/√x)² = 1+2√2

5) (√x-1/√x) =√(1+2√2)