Question

if √5+√7/2√5-3√7=a+b√35 then find A and B ​

Answer 1

Answer:

The answer is $a=-\dfrac{31}{43},b=-\dfrac{5}{43}$

Step-by-step explanation:

Given expression is

      $\dfrac{\sqrt 5+\sqrt 7}{2\sqrt 5-3\sqrt7}$

Rationalize denominator

     $=\dfrac{\sqrt 5+\sqrt 7}{2\sqrt 5-3\sqrt7}\times \dfrac{2\sqrt 5+3\sqrt7}{2\sqrt 5+3\sqrt7}\\\\\\=\dfrac{2(\sqrt 5)^2+3\sqrt 5\times \sqrt 7+2\sqrt 7\times \sqrt 5+3(\sqrt 7)^2}{(2\sqrt 5)^2-(3\sqrt 7)^2}$

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

    $=\dfrac{2(5)+3\sqrt{35}+2\sqrt {35}+3( 7)}{4( 5)-9( 7)}\\\\=\dfrac{10+5\sqrt{35}+21}{20-63}\\\\=\dfrac{31+5\sqrt{35}}{-43}=-\dfrac{31}{43}-\dfrac{5}{43}\sqrt{35}$