if p=2+√5 / 2-√5 and q=2-√5 / 2+√5 , find the values of. (1) p+q (ii)

1 thought on “if p=2+√5 / 2-√5 and q=2-√5 / 2+√5 , find the values of. (1) p+q (ii)”

1. Answer:

   p=2+√5/2-√5

   =(2+√5)(2+√5)/(2-√5)(2+√5)

   =(2+√5)^2/(2^2-√5^2)

   =(2+√5)^2/4-5

   = -(2+√5)^2

   q=2-√5/2+√5

   =(2-√5)(2-√5)/(2+√5)(2-√5)

   =(2-√5)^2/4-5

   = -(2-√5)^2

   I) p+q

   = -(2+√5)^2-(2-√5)^2

   = -(4+5+4√5)-(4+5-4√5)

   =-9-4√5-9+4√5

   = -18

   ii) p-q

   = -(2+√5)^2+(2-√5)^2

   = -(4+5+4√5)+(4+5-4√5)

   = -9-4√5+9-4√5

   = -8√5

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