Question

if a=4/3-√5 find the value of a+4/a​

Answer 1

Answer:

we have,

a= 4/3-√5

so, 1/a = 1/ 4/3-√5

1/a = 1/(4/3-√5)×(4/3+ √5)/ (4/3+√5)

1/a = (4/3 +√5)/ (4/3)²- (√5)²

1/a = (4/3 + √5)/(16/9-5)

1/a =( 4/3+√5)/(-29/5)

1/a = 5(4/3+√5)/-29

1/a = (-5)(4/3+√5)/29

4/a = 4×(-5)(4/3+√5)/29

4/a =( -20)(4/3+√5)/29

Hence, a+4/a = (4/3-√5)+ (-20)(4/3+√5)/29

= 29(4/3-√5)-20(4/3+√5)/ 29

=(116/3- 29√5- 80/3-20√5)/29

=( 36/3-9√5)/29

= (12- 9√5)/29