Question

if x= 2+√3/2-√3 and y = 2-√3/2+√3 find the value of x²+y²-xy​

Answer 1

xy = (2+√3/2-√3) (2-√3/2+√3)

= 4 - √3 + 2√3 + √3 - 3/4 + 3/2 - 2√3 + 3/2 - 3

= 1 - 3/4 + 6/2

= 4 - 3/4

= 12/4

= 3

(x - y) = {(2+√3/2-√3) - (2-√3/2+√3)}

= (2 + √3/2 - √3 - 2 + √3/2 - √3)

= (2√3)/2 - (2√3)

= {(2√3) - 2(2√3)}/2

= -(2√3)/2

= -√3

so,

(x²+y²-xy)

= x²- 2xy +y² + xy

= (x - y)^2 + xy

= (-√3)^2 + 3

= 3 + 3

= 6