Question

find the value of p and q​

Answer 1

Answer:

p = -11/2 and q = -5/2

Step-by-step explanation:

1. First rationalise the equation you will get
2. $\frac{22 + 10 \sqrt{5} }{ - 4}$
3. Now jus compare it with p+q√5 you will get p as -11/2 and q as -5/2

Answer 2

Answer:

p = $-\frac{11}{2}$    and  q = $-\frac{5}{2}$  

Step-by-step explanation:

Here ,

          $\frac{3 +\sqrt{5} }{4-2\sqrt{5} } = p+q\sqrt{5}$

Then , rationalizing we get;

         $\frac{3+\sqrt{5} }{4-2\sqrt{5} } * \frac{4+2\sqrt{5} }{4+2\sqrt{5} } = p+q\sqrt{5}$

     $\frac{3(4+2\sqrt{5}) +\sqrt{5}(4+2\sqrt{5} ) }{(4)^{2} - (2\sqrt{5} )^{2}} = p +q\sqrt{5}$

         $\frac{12+6\sqrt{5}+4\sqrt{5}+10 }{16-20 } = p+q\sqrt{5}$

              $\frac{22+10\sqrt{5} }{-4} = p+q\sqrt{5}$

              $22+10\sqrt{5}$ = $-4p-4q\sqrt{5}$

Comparing the rational with rational and irrational with irrational , we get

  22 = -4p             and                 $q= -\frac{10\sqrt{5} }{4\sqrt{5} }$

$p=-\frac{22}{4}$                                       $q = -\frac{10}{4}$

$p = -\frac{11}{2}$                                        $q = -\frac{5}{2}$     Ans...