Question

answer the question....will be marked brainiest if answered in 2 mins. have arrived till here... 96√7 = a - b√7​...wrong answer will get you reported

Answer 1

Solution:-

$\rm \: \dfrac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} } - \dfrac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} } = a - b \sqrt{7}$

Now take lcm

$\dfrac{(8 + 3 \sqrt{7} )(8 + 3 \sqrt{7} ) - (8 - 3 \sqrt{7} )(8 - 3 \sqrt{7} )}{(8 - 3 \sqrt{7} )(8 + 3 \sqrt{7} )}$

Using this identity

=> ( a + b )(a + b ) = ( a + b )² = a² + b² + 2ab

=>( a - b )² = a² + b² - 2ab

=> ( a + b ) ( a - b ) = ( a² - b² )

We get

$\dfrac{(8 + 3 \sqrt{7}) {}^{2} - (8 - 3\sqrt{7}) {}^{2} }{(8) {}^{2} - (3 \sqrt{7} ) {}^{2} }$

$\dfrac{ {8}^{2} + (3 \sqrt{7} ) {}^{2} + 2 \times 8 \times 3 \sqrt{7} - ({8}^{2} + (3 \sqrt{7} ) {}^{2} - 2 \times 8 \times 3 \sqrt{7} )}{ {8}^{2} - (3 \sqrt{7} ) {}^{2} }$

$\dfrac{64 + 63 + 48 \sqrt{7} - (64 + 63 - 48 \sqrt{7} )}{64 - 63}$

$127 + 48 \sqrt{7} - (127 - 48 \sqrt{7} )$

$127 + 48 \sqrt{7} - 127 + 48 \sqrt{7}$

$48 \sqrt{7} + 48 \sqrt{7}$

$96 \sqrt{7}$

Now

a = 0 and b = -96

Now we have to find

$\rm \sqrt{a - b}$

$\sqrt{0 - ( - 96)}$

$\rm \: \implies \sqrt{96}$