Question

if \frac{3+\sqrt{7}}{3-\sqrt{7}} = a+b\sqrt{7}. find the value of a and b

Answer 1

Solution:

Given:$\frac{3+ \sqrt{7}}{3- \sqrt{7}} = \frac{a+b}{ \sqrt{7}}$

To find: a=?,b=?

by taking conjugate,

$\frac{3+ \sqrt{7}}{3- \sqrt{7}}$ × $\frac{3+ \sqrt{7} }{3+ \sqrt{7}}$

=$\frac{(3+ \sqrt{7})^2}{(3- \sqrt{7} )( 3+\sqrt{7} )}$

=[tex] \frac{(3)^2+( \sqrt{7})^2+2(3)( \sqrt{7})}{(3)^2-( \sqrt{7}^2)} [/tex]

=$\frac{9+7+6 \sqrt{7}}{9-7}$

=[tex] \frac{16+6 \sqrt{7}}{2} [/tex]

=[tex]\frac{2(8+3 \sqrt{7})}{2} [/tex]

=$8+3 \sqrt{7}$

$a+b \sqrt{7}=8+3 \sqrt{7}$

∴ a=8,b=3

 Hope it Helps!!