Question

If x =√3-√2/√3+√2 y=√3+√2/√3-√2 so what is the value of x²+y²+xy

Answer 1

Answer:

We have, x = (√3 - √2 )/(√3 + √2) and y = (√3 + √2) / (√3 - √2)

On rationalising the denominator of x :

X = (√3 - √2 ) × (√3 - √2) /(√3 + √2) (√3 - √2)

x = (√3 - √2)² / (√3 + √2) (√3 - √2)

By Using Identity : (a - b)² = a² + b² - 2ab & (a + b)(a – b) = a² - b²

x = {√3² + √2² - 2 × √3 × √2}/ √3² - √2²

x = {3 + 2 - 2√6}/( 3 - 2)

x = 5 - 2√6 ...........(1)

Now ,

x² = (5 - 2√6)²

By Using Identity : (a - b)² = a² + b² - 2ab

x² = 5² + (2√6)² - 2 × 5 × 2√6

x² = 25 + 24 - 20√6

x² = 49 - 20√6 ............(2)

On rationalising the denominator of y :

y = (√3 + √2) × (√3 + √2)/ (√3 - √2) × (√3 + √2)

y = (√3 + √2)²/(√3 - √2) × (√3 + √2)

By Using Identity : (a + b)² = a² + b² + 2ab & (a + b)(a – b) = a² - b²

y = {√3² + √2² + 2 × √3 × √2}/ √3² - √2²

y = {3 + 2 + 2√6}/( 3 - 2)

y = 5 + 2√6 ............(3)

Now ,

y² = (5 + 2√6)²

By Using Identity : (a + b)² = a² + b² + 2ab

y² = 5² + (2√6)² + 2 × 5 × 2√6

y² = 25 + 24 + 20√6

y² = 49 + 20√6 ............(4)

Now,

From eq 1 & 3 :

xy = (5 - 2√6) ( 5 + 2√6)

By Using Identity : (a + b)(a – b) = a² - b²

xy = 5² - (2√6)²

xy = 25 – 24

xy = 1 ............(5)

Therefore , x² + xy + y²

From eq 2, 4 & 5 :

= 49 - 20√6 + 1 + 49 + 20√6

= 49 + 49 + 1

= 99

x² + xy + y² = 99

Step-by-step explanation:

hope it helps plz mark as brainlist

Answer 2

Answer:

YCYXBOBIGUFT TCU Gogh f