Question

if x = root 3 + root 2 / root 3 - root 2 and y = root 3 - root 2 / root 3 + root 2 , then find the value of x² + y²

Answer 1

Hello Mate!

x = ( √3 + √2 )/( √3 - √2 )
= ( √3 + √2 )/( √3 - √2 ) × ( √3 + √2 )/( √3 + √2 )
= ( √3 + √2 )²/ ( √3² - √2² )
= ( 3 + 2 + 2√6 ) / ( 3 - 2 )
= 5 + 2√6

y = ( √3 - √2 )/( √3 + √2 ) × ( √3 - √2 )/( √3 - √2 )
= ( √3 - √2 )²/( √3² - √2² )
= ( 3 + 2 - 2√6 ) / 1 = 5 - 2√6

x² + y² = ( x + y )² - 2xy
( 5 + 2√6 + 5 - 2√6 ) - 2( 5 + 2√6 )( 5 - 2√6 )
= 10 - 2( 25 - 24 )
= 10 - 2 = 8

Hope it helps