Question

answer the above questions with proper explanation

Answer 1

The answer is given below :

6.

Now,

3 + 2√2

= 1 + 2√2 + 2

= 1² + (2 × 1 × √2) + (√2)²

= (1 + √2)²

So, √(3 + 2√2) = ± (1 + √2)

7.

3 - 2√2

= 1 - 2√2 + 2

= 1² - (2 × 1 × √2) + (√2)²

= (1 - √2)²

So, √(3 - 2√2) = ± (1 - √2)

IDENTITY FORMULA :

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

Thank you for your question.

Answer 2

Hey there!

Let us consider that,
√(3+2√2) = √x + √y

Squaring on both sides,

3 + 2√2 = x + y + 2√xy

x + y = 3 , √xy = 2 .

Now, (x - y)² = (x + y) ² - 4xy = 9 - 8 = 1
x - y = 1 .

So,
x + y = 3
x - y = 1
=========
2x = 4 , x =2

Now, y = 3 -2 =1 .

So finally, √(3+2√2) = √2 + √1 = 1 + √2

*******************************************************

Let us consider that,

√(3-2√2) = √x - √y

Squaring on both sides,

3 - 2√2 = x + y - 2√xy

x + y = 3 , √xy = 2 .

Now, (x - y)² = (x + y) ² - 4xy = 9 - 8 = 1
x - y = 1 .

So,
x + y = 3
x - y = 1
=========
2x = 4 , x =2

Now, y = 3 -2 =1 .

So finally, √(3- 2√2) = √2 - √1 = √2 - 1