friends answer me this questions
If the answer is correct will mark as brainlist
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friends answer me this questions
If the answer is correct will mark as brainlist
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Answer ::
Q3)
[tex] \mathfrak{Solution:} [/tex]
[tex]2x = 3 + \sqrt{7} [/tex]
[tex]x = \frac{3 + \sqrt{7} }{2} [/tex]
Now put this values in this equation,
[tex]\longrightarrow[/tex]
[tex]4 \frac{( 3 + \sqrt{7})^{2} }{2} + \frac{4}{( {3 + \sqrt{7}) }^{2} } [/tex]
[tex]4( \frac{9 +7 + 6 \sqrt{7}) }{4} + \frac{4}{9 + 7 + 6 \sqrt{7} } [/tex]
[tex]16 + 6 \sqrt{7} + \frac{4}{16 + 6 \sqrt{7} } [/tex]
[tex] \frac{256 + 254 + 4}{3 + \sqrt{7} } [/tex]
[tex] \frac{514}{3 + \sqrt{7} } [/tex]
Q4)
x= [tex]\\ \red\bigstar\tt\: \dfrac {√5-√3}{√5+√3}[/tex]
y=[tex]\\ \red\bigstar\tt\: \dfrac {√5+√3}{√5-√3}[/tex]
[tex] {x}^{2} + {y}^{2} = \: to \: find[/tex]
[tex] (\frac{ { \sqrt{5} - \sqrt{3} })^{2} }{ \sqrt{5} + \sqrt{3} } ) + ( \frac{ \sqrt{5} + \sqrt{3^{2} } }{ \sqrt{5 - \sqrt{3} ^{2} } } )[/tex]
[tex] \frac{5 - 3 + 2 \sqrt{3} }{5 + 3 + 2 \sqrt{3} } + \frac{5 + 3 + 2 \sqrt{3} }{5 + 3 - 2 \sqrt{3} } [/tex]
[tex] \frac{2 + 2 \sqrt{3} }{8 + 2 \sqrt{3} } + \frac{8 + 2 \sqrt{3} }{2 + 2 \sqrt{3} } [/tex]
[tex] \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}) } [/tex]
[tex] \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 } [/tex]
[tex] \frac{92 + 40 \sqrt{2} }{28 + 18 \sqrt{3} } [/tex]
[tex] \frac{2(46 + 20 \sqrt{3}) }{2(14 + 9 \sqrt{3}) } [/tex]
[tex]final \: answer = \frac{46 + 20{ \sqrt{3} } }{14 + 9 \sqrt{3} } [/tex]
Q3)
[tex]\huge\sf\green{Answer}[/tex]
solution:
[tex]\longrightarrow[/tex]
[tex] \frac{3 \sqrt{2} - 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } + \frac{2 \sqrt{3} }{ \sqrt{3} - \sqrt{2} } [/tex]
[tex] \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} )} [/tex]
[tex] \frac{ 3 \sqrt{6} - 6 \sqrt{6} + 12 }{3 \sqrt{6} + 6 - 12 - 2 \sqrt{6} } [/tex]
[tex] \frac{ - 3 \sqrt{6} + 12 }{ \sqrt{6} - 6 } [/tex]
[tex] \frac{ - 3 \sqrt{6} + 12 }{ \sqrt{6} - 6} \times - \frac{3 \sqrt{6} - 12 }{ \sqrt{6} - 6} [/tex]
[tex] = 11[/tex]