Question

if x = √3+√2 / √3-√2 and y = √3-√2 / √3+√2 , find x² + y²​

Answer 1

Answer:

{(√3+√2 )/ (√3-√2) }^2 + {( √3-√2)/√3+√2)}^2

= {(3+2+2√6)/(3+2-2√6)} + {(3+2-2√6)/(3+2+2√6)}

={(5+2√6)/(5-2√6)} + {(5-2√6)/(5+2√6)}

= {(5+2√6)^2 + (5-2√6)^2}\{(5-2√6)(5+2√6)}

=(25+24+20√6+25+24-20√6)/(25-24)

=25+24+25+24=98.