Question

If a=3+√5, THEN a² +1/a2=​

Answer 1

Answer:

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

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