Question

Ques 7 : If a=(3+V5)/2 , find the
value of a²+1/a?

Answer 1

Step-by-step explanation:

a=(3+√5)/2

(1/a)=(2)/(3+√5)

={(2)(3-√5)}/{(3+√5)(3-√5)}

={(2)(3-√5)}/(9-5)

={(2)(3-√5)}/4

=(3-√5)/2

a^2+(1/a)={(3+√5)/(2)}^2+(3-√5)/2

=(9+5+6√5+6-2√5)/4

=(20+4√5)/4

=4(5+√5)/4

=5+√5

{a+(1/a)}^2= a^2 + (1/a)^2 +2

a^2 + (1/a)^2 =[{(3+√5)/2}+{(3-√5)/2}]^2 - 2

=[(6/2)^2]-2

=(3)^2-2

=7