Question

give ma a answer for a question​

Answer 1

Answer:

Note that

${x}^{2} + {y}^{2} \\ = 23 + 4 \sqrt{33} + 23 - 4 \sqrt{33} \\ = 46 \\ \\ {x}^{2} - {y}^{2} \\ = 8 \sqrt{33} \\ \\ \\ xy \\ = \sqrt{{23}^{2} - (4 \sqrt{33} ) {}^{2} } \\ = \sqrt{529 - 528} \\ = 1$

Now just use equalities and put values .

$\frac{ {x}^{3}{ - {y}^{3} } }{x + y} \\ \\ = \frac{(x - y)( {x}^{2} + {y}^{2} + xy)}{x + y} \\ \\ = \frac{(x - y)(46 + 1)}{x + y} \times \frac{x - y}{x - y} \: \: \: \{ \: rationalization \\ \\ = \frac{47(x - y) {}^{2} }{ {x}^{2} - {y}^{2} } \\ \\ = \frac{47( {x}^{2} + {y}^{2} - 2xy) }{8 \sqrt{33} } \\ \\ = \frac{47(46 - 2)}{8 \sqrt{33} } \times \frac{ \sqrt{33} }{ \sqrt{33} } \\ \\ = \frac{47 \times44 \times \sqrt{33} }{8 \times 33 } \\ \\ = \frac{47 \sqrt{33} }{6}$