Math, asked by prateekpandit9, 10 months ago

Help me please guys​

Attachments:

Answers

Answered by AlluringNightingale
3

Answer :

x² + y² + xy = 624

Solution :

→ Given : x = (√3 - √2)/(√3 + √2)

y = (√3 + √2)/(√3 - √2)

→ To find : x² + y² + xy

We have ;

x = (√3 - √2)/(√3 + √2)

Now ,

Rationalising the denominator , we have ;

=> x = (√3-√2)(√3-√2) / (√3+√2)(√3-√2)

=> x = (√3 - √2)² / [ (√3)² - (√2)² ]

=> x = (√3 - √2)² / (3 - 2)

=> x = (√3 - √2)² /1

=> x = (√3 - √2)²

=> x = (√3)² + (√2)² - 2•√3•√2

=> x = 3 + 2 - 2√6

=> x = 5 - 2√6

Also ,

y = (√3 + √2)/(√3 - √2)

Now ,

Rationalising the denominator , we have ;

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

=> y = (√3 + √2)² / [ (√3)² - (√2)² ]

=> y = (√3 + √2)² / (3 - 2)

=> y = (√3 + √2)² /1

=> y = (√3 + √2)²

=> y = (√3)² + (√2)² + 2•√3•√2

=> y = 3 + 2 + 2√6

=> y = 5 + 2√6

Also ,

xy = 1 as x and y are reciprocal of each other .

Now ,

=> x² + y² + xy

= x² + y² + 2xy - xy

= (x² + 2xy + y²) - xy

= (x + y)² - xy

= (5 - 2√6 + 5 + 2√6)² - 1

= 25² - 1

= 625 - 1

= 624

Hence ,

x² + y² + xy = 624

Similar questions