Question

find the value of a and b: √7+1/√7-1 + √7-1/√7+1 = a-b√7​

Answer 1

Answer:

a = 8/3 and b = 0

Step-by-step explanation:

$\frac{ \sqrt{7} + 1 }{ \sqrt{7} - 1 } + \frac{ \sqrt{7} - 1 }{ \sqrt{7} + 1 }$

Rationalizing the denominators we get:

$\frac{ \sqrt{7} + 1}{ \sqrt{7} - 1 } \times \frac{ \sqrt{7} + 1}{ \sqrt{7} + 1} + \frac{ \sqrt{7} - 1 }{ \sqrt{7} + 1 } \times \frac{ \sqrt{7} - 1 }{ \sqrt{7} - 1 }$

$= \frac{ {( \sqrt{7}) }^{2} + {(1)}^{2} + 2. \sqrt{7}.1 }{ {( \sqrt{7}) }^{2} - {(1)}^{2} } + \frac{ {( \sqrt{7}) }^{2} + {(1)}^{2} - 2. \sqrt{7} .1}{ {( \sqrt{7} )}^{2} - {(1)}^{2} }$

$= \frac{7 + 1 + 2 \sqrt{7} }{7 - 1} + \frac{7 + 1 - 2 \sqrt{7} }{7 - 1} \\ \\ = \frac{8 + 2 \sqrt{7} + 8 - 2 \sqrt{7} }{6} \\ \\ = \frac{16}{6} \\ \\ = \frac{8}{3}$

$a - b \sqrt{7} = \frac{8}{3} \\ \\ \bf a = \frac{8}{3} \: \: and \: \: b = 0$