Question

if a = root 5 + 3 / root 5 -3 and b = root 5 - 3 / root 5 + 3 , find the value of a ^2 + b^2 + ab

Answer 1

Answer:

a=(√5+3)/(√5-3)

b=(√5-3)/(√5+3)

ab=(√5+3)/(√5-3)×(√5-3)/(√5+3)=1

a+b=(√5+3)/(√5-3)+(√5-3)/(√5+3)

=(√5+3)^2+(√5-3)^2/(√5+3)((√5-3)

=(5+9+6√5+5+9-6√5)/(√5^2-3^2)

=28/(5-9)

=28/-4

= -7

a^2+b^2+ab

=(a+b)^2-2ab+ab

=(-7)^2-ab

= 49-1

= 48

Hope it helps!!