Question

a^4+1/a^4=723 then a^3-1/a^3=?
with process​

Answer 1

Answer:

a³ + 1/a³ = 198

a³ + 1/a³ = 198a⁴ + 1/a⁴ = 1154

Step-by-step explanation:

First, work out

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.Cubing (**) give

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.Cubing (**) give6³ = ( a + 1/a )³ = a³ + 3 a² (1/a) + 3 a (1/a)² + 1/a³

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.Cubing (**) give6³ = ( a + 1/a )³ = a³ + 3 a² (1/a) + 3 a (1/a)² + 1/a³= a³ + 3a + 3/a + 1/a³

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.Cubing (**) give6³ = ( a + 1/a )³ = a³ + 3 a² (1/a) + 3 a (1/a)² + 1/a³= a³ + 3a + 3/a + 1/a³= a³ + 1/a³ + 3 ( a + 1/a )

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.Cubing (**) give6³ = ( a + 1/a )³ = a³ + 3 a² (1/a) + 3 a (1/a)² + 1/a³= a³ + 3a + 3/a + 1/a³= a³ + 1/a³ + 3 ( a + 1/a )= a³ + 1/a³ + 3 ( 6 ).

First, work outa + 1/a = 3 + 2√2 + 1 / ( 3 + 2√2 )= 3 + 2√2 + ( 3 - 2√2 ) / ( 9 - 8 )= 3 + 2√2 + 3 - 2√2= 6. (**)Now square to get6² = ( a + 1/a )² = a² + 2 a (1/a) + 1/a² = a² + 1/a² + 2,so a² + 1/a² = 36 - 2 = 34. (****)We weren't asked for that one, but that sets the stage.Cubing (**) give6³ = ( a + 1/a )³ = a³ + 3 a² (1/a) + 3 a (1/a)² + 1/a³= a³ + 3a + 3/a + 1/a³= a³ + 1/a³ + 3 ( a + 1/a )= a³ + 1/a³ + 3 ( 6 ).so a⁴ + 1/a⁴ = 34² - 2 = 1154.

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