Question

If a=3-root 5,find the value of a+1/a

Answer 1

Answer:

7

Step-by-step explanation:

a = 3 +∫5 / 2

Therefore, 1 / a = 2 / 3 + ∫5

= 2 × ( 3 -  √5 ) / ( 3 + ∫5 ) × ( 3 - ∫ 5 )

= 2 × ( 3 -  √5 )  / ( 3 ) ^ 2 - ( √5 ) ^ 2

= 3 - √5 / 2

a + 1 /a = 3+√5 /2 +  3-√5 /2

         =  6 / 2  

         = 3

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

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

= ( 3) ^2 - 2 = ( a + 1 /a )^2 + 2 (a)(1/a) - 2   ( Adding and subtracting 2 on both  sides )

9 -2 = ( a + 1 /a )^2

= 7 .

Therefore, (a + 1/a)^2 = 7

Answer 2

Answer:

5/3-√5

Step-by-step explanation:

or a+1/a

or a=3-√5

or 3-√5+1/3-√5

or 9-√25+1/3-√5

or 9-5+1/3-√5

or 10-5/3-√5

or 5/3-√5