Question

lf x=√3+1/√3+1 and y=√3-1/√3+1, find the value of x^2+xy+y^2.

Answer 1

Sol :

Given x = (√3+1) / (√3-1) ( rationalize numerator and denominator by (√3+1) )

x = (√3+1)2 / (3-1) ⇒ 4 + 2√3 / 2 = 2 + √3 square on both sides then

x2 = 7 + 4√3

y = (√3-1) / (√3+1) ( rationalize numerator and denominator by (√3 -1) )

y = (√3-1)2 / (3-1) ⇒ 4 - 2√3 / 2 = 2 - √3 square on both sides then

y2 = 7 - 4√3

xy = (2 + √3)(2 - √3) = 1

Nowx2+ xy + y2 = 7 + 4√3 +1 + 7 - 4√3 = 15 .