If a=3+root5÷2 thenbfind the value of a2+1÷a2
Answers
Answered by
2
a= (3+√5)/2
a^2={(3+√5)^2}/2
={(3)^2+(√5)^2+2(3)(√5)}/(2)^2
={9+5+6√5}/4
={14+6√5}/4
={7+3√5}/2
(a^2+1)/a^2
=[({7+3√5)/2}+1]/[(7+3√5)/2]
=[(7+3√5+2)/2]/[(7+3√5)/2]
=[(9+3√5)/2]/[(7+3√5)/2]
=[9+3√5]/[7+3√5]
If you want to further rationalize the denominator,then
=(9+3√5)(7-3√5)/(7+3√5)(7-3√5)
=(63-27√5+21√5-15)/(49-45)
=(48-6√5)/4
=12+{(3√5)/2}
a^2={(3+√5)^2}/2
={(3)^2+(√5)^2+2(3)(√5)}/(2)^2
={9+5+6√5}/4
={14+6√5}/4
={7+3√5}/2
(a^2+1)/a^2
=[({7+3√5)/2}+1]/[(7+3√5)/2]
=[(7+3√5+2)/2]/[(7+3√5)/2]
=[(9+3√5)/2]/[(7+3√5)/2]
=[9+3√5]/[7+3√5]
If you want to further rationalize the denominator,then
=(9+3√5)(7-3√5)/(7+3√5)(7-3√5)
=(63-27√5+21√5-15)/(49-45)
=(48-6√5)/4
=12+{(3√5)/2}
Similar questions