Question

friends answer me this questions
If the answer is correct will mark as brainlist ​

Answer 1

Answer:

Answer ::

Q3)

$\mathfrak{</u><u>S</u><u>o</u><u>l</u><u>u</u><u>t</u><u>i</u><u>o</u><u>n</u><u>:</u><u>}$

$2x = 3 + \sqrt{7}$

$x = \frac{3 + \sqrt{7} }{2}$

Now put this values in this equation,

$\longrightarrow$

$4 \frac{( 3 + \sqrt{7})^{2} }{2} + \frac{4}{( {3 + \sqrt{7}) }^{2} }$

$4( \frac{9 +7 + 6 \sqrt{7}) }{4} + \frac{4}{9 + 7 + 6 \sqrt{7} }$

$16 + 6 \sqrt{7} + \frac{4}{16 + 6 \sqrt{7} }$

$\frac{256 + 254 + 4}{3 + \sqrt{7} }$

$\frac{514}{3 + \sqrt{7} }$

Q4)

x= $\\ \red\bigstar\tt\: \dfrac {√5-√3}{√5+√3}$

y=$\\ \red\bigstar\tt\: \dfrac {√5+√3}{√5-√3}$

${x}^{2} + {y}^{2} = \: to \: find$

$(\frac{ { \sqrt{5} - \sqrt{3} })^{2} }{ \sqrt{5} + \sqrt{3} } ) + ( \frac{ \sqrt{5} + \sqrt{3^{2} } }{ \sqrt{5 - \sqrt{3} ^{2} } } )$

$\frac{5 - 3 + 2 \sqrt{3} }{5 + 3 + 2 \sqrt{3} } + \frac{5 + 3 + 2 \sqrt{3} }{5 + 3 - 2 \sqrt{3} }$

$\frac{2 + 2 \sqrt{3} }{8 + 2 \sqrt{3} } + \frac{8 + 2 \sqrt{3} }{2 + 2 \sqrt{3} }$

$\frac{2(2 + 2 \sqrt{3}) + 2 \sqrt{3} (2 + 2 \sqrt{3} ) + 8(8 + 2 \sqrt{3} ) + 2 \sqrt{3} (8 + 2 \sqrt{3}) }{2(8 + 2\sqrt{3} ) + 2 \sqrt{3} (8 + 2\sqrt{3}) }$

$\frac{4 + 4 \sqrt{3} + 4 \sqrt{3} + 12 + 64 + 16 \sqrt{3} + 16 \sqrt{3} + 12}{16 +2 \sqrt{3} + 16 \sqrt{3} + 12 }$

$\frac{92 + 40 \sqrt{2} }{28 + 18 \sqrt{3} }$

$\frac{2(46 + 20 \sqrt{3}) }{2(14 + 9 \sqrt{3}) }$

$final \: answer = \frac{46 + 20{ \sqrt{3} } }{14 + 9 \sqrt{3} }$

Q3)

$\huge\sf\green{Answer}$

solution:

$\longrightarrow$

$\frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} }$

$\frac{ \sqrt{3}(3 \sqrt{2} - 2\sqrt{3} ) + 2 \sqrt{3}(3 \sqrt{2} + 2 \sqrt{3} }{ \sqrt{3}(3 \sqrt{2 } + 2 \sqrt{3} ) - \sqrt{2} (3 \sqrt{2} + 2 \sqrt{3} )}$

$\frac{ 3 \sqrt{6} - 6 \sqrt{6} + 12 }{3 \sqrt{6} + 6 - 12 - 2 \sqrt{6} }$

$\frac{ - 3 \sqrt{6} + 12 }{ \sqrt{6} - 6 }$

$\frac{ - 3 \sqrt{6} + 12 }{ \sqrt{6} - 6} \times - \frac{3 \sqrt{6} - 12 }{ \sqrt{6} - 6}$

$= 11$