Question

If a-1÷a=3 find a^2+1÷a^2 and a^3-1÷a^3​

Answer 1

hope this is helpful..

Answer 2

Answer:

The value of a² + ( 1 / a² ) is 11.

The value of a³ + ( 1 / a³ ) is 36.

Step-by-step-explanation:

We have given that,

a - ( 1 / a ) = 3

We have to find the value of

a² + ( 1 / a² ) and a³ - ( 1 / a³ ).

Now,

a - ( 1 / a ) = 3

By squaring both sides, we get,

[ a - ( 1 / a ) ]² = 3²

We know that,

( x - y )² = x² - 2xy + y²

⇒ a² + ( 1 / a² ) - 2 * a * 1 / a = 9

⇒ a² + ( 1 / a² ) - 2 = 9

⇒ a² + ( 1 / a² ) = 9 + 2

⇒ a² + ( 1 / a² ) = 11

∴ The value of a² + ( 1 / a² ) is 11.

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Now,

a + ( 1 / a ) = 3

By cubing both sides, we get,

[ a + ( 1 / a ) ]³ = 3³

We know that,

( x - y )³ = x³ - 3x²y + 3xy² - y³

⇒ a³ - 3 * a² * ( 1 / a ) + 3 * a * ( 1 / a )² - ( 1 / a )³ = 27

⇒ a³ - 3 * a + 3 * a * 1 / a² - ( 1 / a³ ) = 27

⇒ a³ - 3a + ( 3 / a ) - ( 1 / a³ ) = 27

⇒ a³ - ( 1 / a³ ) - 3 [ a - ( 1 / a ) ] = 27

⇒ a³ - ( 1 / a³ ) - 3 * 3 = 27

⇒ a³ - ( 1 / a³ ) - 9 = 27

⇒ a³ - ( 1 / a³ ) = 27 + 9

⇒ a³ - ( 1 / a³ ) = 36

∴ The value of a³ + ( 1 / a³ ) is 36.