Question

Find the value of x^2+y^2+xy

Answer 1

On rationalising "x" and "y"

We get,

$x = 2 + \sqrt{3} \\ y = 2 - \sqrt{3} \\ \\ {x}^{2} + {y}^{2} + xy \\ = {(2 + \sqrt{3)} }^{2} + {(2 - \sqrt{3)} }^{2} + (2 - \sqrt{3} )(2 + \sqrt{3} ) \\ = 4 + 3 + 2 \sqrt{3} + 4 + 3 - 2 \sqrt{3} + 4 - 3 \\ = 4 + 3 + 4 + 3 + 1 \\ \\ = 15$

HOPE that it will help you ✌️ ✌️

Answer 2

Answer: 12.

The full answer is in the attachment.

I've used identities in this question like,

(a+b)^2=a^2+b^2+2ab

(a-b)^2=a^2+b^2-2ab

(a+b)(a-b)=a^2-b^2.

where, a and b are rational numers.

If you have any doubt, feel free to ask in the comment section.

$<marquee>Th@nk y0u$