Question

x=(3-2√2)show that {√x-1/√x}​

Answer 1

Answer:

3

Step-by-step explanation:

If x=3-2 root 2

Therefore 1/x={1/(3-2root 2)}×{(3+2root2)/3+2root2)}

=(3+2root2)/(3)^2-(2root2)^2=3+root 2 {By rationalizing the denominator}

Now,

(x+1/x)=(root x-1/root x)^2+2

(3-2root2+3+2root2)=(root x-1/root x)^2+2

6=(root x-1/root x)^2+2

6-2=(root x+1/root x)^2

4=(root x+1/root x)^2

Square Rooting both sides

root 4=(root x+1/root x)

(root x+1/root x)=2