Question

plz help me with this question..plz ​

Answer 1

Here's ur answer

hope it helped u

Answer 2

Answer:

$x = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ \\ = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \times\frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \\ \\ = \frac{ (\sqrt{3}- \sqrt{2}) {}^{2} }{ (\sqrt{3} ) {}^{2} - ( \sqrt{2} ) {}^{2} } = \frac{3 + 2 - 2 \sqrt{3} \sqrt{2} }{3 - 2} \\ \\ = \frac{5 - 2 \sqrt{6} }{1} = 5 - 2 \sqrt{6}$

Similarly ,

$y = 5 + 2 \sqrt{6}$

So,

${x}^{2} + {y}^{2} + xy \\ \\ = (5 - 2 \sqrt{6} ) {}^{2} + (5 + 2 \sqrt{6} ) {}^{2} + (5 - 2 \sqrt{6} )(5 + 2 \sqrt{6} ) \\ = (25 + 24 - 20 \sqrt{6} )+ (25 + 24 + 20 \sqrt{6} ) + (25 - 24) \\ = </strong><strong>4</strong><strong>9</strong><strong> +</strong><strong>49</strong><strong> + 1 = </strong><strong>9</strong><strong>9$