Question

if p=2+√5 / 2-√5 and q=2-√5 / 2+√5 , find the values of. (1) p+q (ii) p-q (ii) p²+q²
(IV) p²-q​

Answer 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