If x = and y = , then x 2 + x y + y 2 =

Question

Philoid · Accepted Answer

Given x = , y =

X= 5 – 2√6

X² = (5 – 2√6)² = 25 +24 -20√6) = 49 – 20√6

Similarily y = = 5 + 2√6

Y² = (5 + 2√6 )² = 49 + 20√6

Xy = (5- 2√6) ( 5 + 2√6) = 25 – 24 = 1

So, x²+ xy+y² = 49 – 20√6 +1 + 49 + 20√6 = 99.