Question

if p=(2-√5)/(2+√5) and q=(2+√5)/(2-√5), find (p-q)

Answer 1

Hello Mate!

$p = \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \\ \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } \\ = \frac{4 + 5 - 4 \sqrt{5} }{4 - 5} = 4 \sqrt{5} - 9 \\ \\ q = \frac{2 + \sqrt{5} }{2 - \sqrt{5} } \\ = \frac{2 + \sqrt{5} }{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} } \\ = \frac{4 + 5 + 4 \sqrt{5} }{4 - 5} = - 9 - 4 \sqrt{5} \\ \\ p - q \\ = (4 \sqrt{5} - 9) - ( - 9 - 4 \sqrt{5} ) \\ = 4 \sqrt{5} - 9 + 9 + 4 \sqrt{5} \\ = 8 \sqrt{5}$

Have great future ahead!

Answer 2

p-q=(2-√5)/(2+√5) - (2+√5)/(2-√5)

    =2-√5  -  2+√5

      2+√5    2-√5

    =2-√5-2-√5

      (2²)-(√5)²

     =  -2√5  

          4-5

    = -2√5

       -1

   = +2√5 Answer

HOPE YOU UNDERSTAND.

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