Help me please guys
Answers
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