Question

x=root 5 - root 2 /root 5 + root 2
y=root 5 + root 2 /root 5 - root 2
find value of x^2+xy+y^2​

Answer 1

Step-by-step explanation:

x=(√5-√2)/(√5+√2)=(7-2√(10))/3. (1) ( by rationalization)

y=(√5+√2)/(√5-√2)=(7+2√(10))/3. (2)

Find:-

x^2+xy+y^2

={(7-2√10)/3}^2+1+{7+2√10)/3}^2. [ by (1) &(2) xy=1]

={(89-28√10)/9}+{(89+28√10)/9}+1

=178/9+1

=187/9