Question

if 3 + under root 7 / 3 minus root 7 is equal to a+b under root 7 then a
, b is equal to

Answer 1

Heya !!!

Identities used :

${(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ (x + y)(x - y) = {x}^{2} - {y}^{2}$



L.H.S
$= \frac{3 + \sqrt{7} }{3 - \sqrt{7} }$

On rationalizing the denominator we get,

$= \frac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \frac{3 + \sqrt{7} }{3 + \sqrt{7} } \\ \\ = \frac{ {(3 + \sqrt{7} )}^{2} }{(3 - \sqrt{7})(3 + \sqrt{7}) } \\ \\ = \frac{ {(3)}^{2} + {( \sqrt{7} )}^{2} + 2(3)( \sqrt{7} ) }{ {(3)}^{2} - {( \sqrt{7} )}^{2} } \\ \\ = \frac{9 + 7 + 6 \sqrt{7} }{9 - 7} \\ \\ = \frac{16 + 6 \sqrt{7} }{2} \\ \\ = 8 + 3 \sqrt{7}$

On comparing both sides we get

8 + 3√7 = a + b√7

a = 8 : b = 3

Hope this helps ☺