Question

find the value of a and b √7 - 5 / √7 + 5 = a + b √35​

Answer 1

AnsWer :

a = -6 and b = 1.

Correct Question :

Find the value of a and b where, √7 - √5 / √7 + √5 = a + b√35.

Solution :

$\tt\longmapsto \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} }$

Rationalizing the denominator,

$\tt \longmapsto \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} } \times \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} - \sqrt{5} }$

$\tt \longmapsto \frac{ {( \sqrt{7} - \sqrt{5} )}^{2} }{ { \sqrt{(7)} }^{2} - { \sqrt{(5)} }^{2} }$

$\tt \longmapsto \frac{7 + 5 - 2 \sqrt{35} }{7 - 5}$

$\tt \longmapsto \frac{12 - 2 \sqrt{35} }{2}$

$\tt \longmapsto \frac{2(6 - \sqrt{35}) }{2}$

$\tt \longmapsto 6 - \sqrt{35}$

Taking negative sign common we get,

$\tt \longmapsto - 6 + \sqrt{35} .$

So, We can Say that,

$\tt \mapsto a = - 6 \: \: and \: \: b = 1.$

Therefore, the value of a be -6 and b = 1.