Question

pls tell fast guys pls

Answer 1

Answer:

$\: {\large{\pmb{\sf{★Given...}}}}$

${ \sf{ \frac{ \sqrt{7} - 1}{ \sqrt{7} + 1} - \frac{ \sqrt{7} + 1 }{ \sqrt{7} - 1} = a + b \sqrt{7} }}$

$\: {\large{\pmb{\sf{★To \: Find...}}}}$

Value of a and b..?

$\: {\large{\pmb{\sf{★Used \: Formula...}}}}$

(a² - b²) = (a + b) (a -b)

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

$\: {\large{\pmb{\sf{★Solution...}}}}$

By doing LCM,

$: \implies{ \sf{ \frac{ \sqrt{7} - 1}{ \sqrt{7} + 1} - \frac{ \sqrt{7} + 1 }{ \sqrt{7} - 1} }}$

$: { \implies { \sf{ \frac{ {( \sqrt{7 } - 1) }^{2} - {( \sqrt{7} + 1) }^{2} }{( \sqrt{7} + 1)( \sqrt{7} - 1)} }}}$

$\: : { \implies { \sf{ \frac{ {( \sqrt{7} ) }^{2} + {(1)}^{2} - 2( \sqrt{7})(1) - ( { \sqrt{7}) }^{2} + {1}^{2} + 2( \sqrt{7} )(1)}{ { \sqrt{(7}) }^{2} - {(1)}^{2} } }}}$

$\: : { \implies { \sf{ \frac{7 + 1 - 2 \sqrt{7} - (7 + 1 + 2 \sqrt{7}) }{7 - 1} }}}$

$\: : { \implies { \sf{ \frac{8 - 2 \sqrt{7} - (8 + 2 \sqrt{7} )}{6} }}}$

$\: : { \implies { \sf \frac{8 - 2 \sqrt{7} - 8 - 2 \sqrt{7} }{6} {}}}$

$: { \implies{ \sf{ \frac{ - 2 \sqrt{7} - 2 \sqrt{7} }{6} }}}$

$\: : { \implies{ \sf{ \frac{ - 4 \sqrt{7} }{6} }}}$

$\: : { \implies{ \sf{ \frac{ - \cancel{ \: {4}}^{2} ( \sqrt{7}) }{ \cancel{ {6}}^{3} } }}}$

$\: : { \implies{ \sf{ \frac{ - 2 \sqrt{7} }{3} }}}$

Comparing -2√7/3 with a + b√7

We get,

• a = 0
• b = -2/3

$\: {\large{\pmb{\sf{★Final \: Answer...}}}}$

Therefore, a = 0 , b = -2/3

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