Question

√7 -√6 / √7+√6 , solve

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} + \sqrt{6} }$

on rationalizing, we get

$\frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} + \sqrt{6} } \times \frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} - \sqrt{6} }$

Using identities,

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ (a + b)(a - b) = {a}^{2} - {b}^{2}$

we get,

$\frac{ {( \sqrt{7}) }^{2} + {( \sqrt{6} )}^{2} + 2 \times \sqrt{7} \times \sqrt{6} }{ {( \sqrt{7} )}^{2} - {( \sqrt{6}) }^{2} } \\ \\ = \frac{7 + 6 + 2 \sqrt{42} }{7 - 6} \\ \\ = 13 + 2 \sqrt{42}$


Hope this helps!!!

@Mahak24

Thanks...
☺

Answer 2

√7-√6÷√7+√6
(√7-√6)(√7-√6)÷(√7+√6)(√7-√6)
(√7-√6)^2÷(7-6)
7+6-2√42
13-2√42 ans