Question

plz answer this i will mark u brainliest​

Answer 1

Answer:

a = - 9  and  b = - 4

Step-by-step explanation:

  $\dfrac{2+\sqrt5}{2-\sqrt5}$ = a + b√5

Solving LHS :

$\implies\dfrac{2+\sqrt5}{2-\sqrt5}$

   Multiply as well as divide by 2 + √5:

$\implies\dfrac{2+\sqrt5}{2-\sqrt5}\times\dfrac{2+\sqrt5}{2+\sqrt5}\\\\\\\implies\dfrac{(2+\sqrt5)^2}{(2+\sqrt5)(2-\sqrt5)}$

    For numerator use ( a + b )^2 = a^2 + b^2 + 2ab and for denominator use ( a + b )( a - b ) = a^2 - b^2

$\dfrac{2^2 + (\sqrt5)^2 +2( 2\times \sqrt5)}{2^2 - (\sqrt5)^2}\\\\\\\implies \dfrac{4+5+ 4 \sqrt5}{4-5}\\\\\\\implies\dfrac{9+4\sqrt5}{-1}\\\\\\\implies - 9 - 4 \sqrt5$

 

  Hence,

⇒ - 9 - 4√5 = a + b√5

    Comparing values :

⇒ a = - 9    and    b = - 4