Question

If x = 3 + 2 √2, find the value of [√x - 1 (8)√x]

plz ans it fast.

the correct answer will be marked as brainlist.

I want explanation also​.

Answer 1

Answer:

x= 3+2√2

Identity = (a+b)²= a²+b²+2ab

2√2 is 2ab part.

2√2= 2ab

ab = √2

3 must be a²+b²

possibilities of a and b

a= 1,b=√2 or vice versa

a² = 1²= 1

b²= (√2)² = 2

1+2 = 3

therefore

3+2√2 = (1+√2)²

√x = √3+2√2

= √(1+√2)²

= 1+√2

√x+1/√x

= 1+√2 +1/1+√2

1/√x=

by rationalising

1/1+√2× 1-√2/1-√2

Identity - (a+b)(a-b) = a²-b²

= (1-√2)/1²-(√2)²

= (1-√2)/1-2

(1-√2)/-1

= -(1-√2)

= -1+√2

√x+1/√x=

1+√2-1+√2

1 gets cancelled.

= 2√2.