Question

if x is equal to root 5 + root 3 by root 5 minus root 3 and Y is equals to root 5 minus root 3 by root 5 + root 3 then find the value of x square + Y square + x y​

Answer 1

Answer:

Step-by-step explanation:

x = √5 +√3/√5-√3

Rationalise

√5 +√3/√5-√3 × √5 +√3/√5+√3

5+ √15 +√15 +3 / 5-3

8 + 2√15 /2

4 +√15

x = 4 +√15

y = √5 -√3/√5+√3

Rationalise

√5 -√3/√5+√3 × √5 -√3/√5-√3

5- √15 -√15 -3 / 5-3

2 -  2√15 /2

1-√15

y = 1 - √15

x² + y²+ xy

= (4+√15)²+ (1- √15)² + 2 (4+√15)(1- √15)

= 31 -14 + 2 (4 - 4√15 +√15-15)

= 31 -14 +2 (-11 -3√15)

= 17 - 22 - 6√15

= -5 -6√15