Question

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

Answer 1

Answer:

99

Step-by-step explanation

x=√3+√2/√3-√2   y=√3-√2/√3+√2

x²+y²+xy =?

x=(√3+√2/√3-√2)(√3+√2/√3+√2) = 3+2+2√6/3-2 = 5+2√6

y=(√3-√2/√3+√2)(√3-√2/√3-√2) = 3+2-2√6/3-2 =  5-2√6

(5+2√6)² + (5-2√6)² + (5+2√6)(5-2√6)

25 + 24 + 20√6 + 25 + 24 - 20√6 + 25 - 24

99