Math, asked by Anonymous, 8 months ago

Q:-Find the value of a and b
 \sqrt{a - b}
if
 \frac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} } - \frac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} } = a + b \sqrt{7}

Answers

Answered by Anonymous
2

Step-by-step explanation:

\red{\bold{\underline{\underline{❥Question᎓}}}}

Q:-Find the value of

 \sqrt{a - b}

if

 \frac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} } - \frac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} } = a + b \sqrt{7}

\huge\tt\underline\blue{⛶Answer⛶</p><p> }

╔════════════════════════╗

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _✍️

⟹ \frac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} }  -  \frac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} }  = a + b \sqrt{7}

⟹ \frac{(8 + 3 \sqrt{7})(8 + 3 \sqrt{7}) - [(8 - 3 \sqrt{7}  )(8 - 3 \sqrt{7}) ]}{(8 + 3 \sqrt{7} )(8 - 3 \sqrt{7} )} =a+b√7

 {(a + b)}^{2}  - {(a - b)}^{2}  = 4ab

⟹ \frac{4 \times 8 \sqrt{7} }{ {(8)}^{2}  -  {(3 \sqrt{7}) }^{2} }  = a + b \sqrt{7}

⟹ \frac{32 \sqrt{7} }{64 - 63}  = a + b \sqrt{7}

⟹ \frac{32 \sqrt{7} }{1}  = a + b \sqrt{7}

⟹32 \sqrt{7}  = a + b \sqrt{7}

⟹0 + 32 \sqrt{7}  = a + b \sqrt{7}

On comparing both sides:-

⟹a = 0 \: and \: b = 32

⟹now \:  \sqrt{a - b}  =  \sqrt{0 - 32}  =  \sqrt{ - 32 }  =  \sqrt{ - 2 \times 16}  = 4 \sqrt{ - 2}  = 4 \sqrt{2} i \:   [( {i}^{2}  =  - 1)]

╚════════════════════════╝

нσρє ıт нєłρs yσυ

_____________________

тнαηkyσυ

Similar questions