Question

If x is equal to the square root 5 minus square root 2 divided by square root 5 plus square root 2 and y is equal to the square root 5 plus square root 2 divided by square root 5 minus square root 2 find the value of x² +xy+y²

Answer 1

Answer:

187/3

Step-by-step explanation:

x is equal to the square root 5 minus square root 2 divided by square root 5 plus square root 2

x = (√5 - √2) ÷ ( √5 +√2) = (7 - 2√10)÷3

y is equal to the square root 5 plus square root 2 divided by square root 5 minus square root 2

y = (√5 + √2) ÷ ( √5 -√2) = (7 +2√10)÷3

x+y = 14/3 , xy = 49 - 40 ÷ 9 = 1

x² +xy+y² = (x+y)² - xy = 196/9 - 1 = 187/3