Question

Hi, I'm stuck with this question for a while but I still can't solve it. Is anyone can solve this, please?
If x+\frac{1}{x} = 2\sqrt{3} then what is (x^{3} - \frac{1}{x^{3}})?

Answer 1

Heya!!!

WE KNOW THAT

a³ - b³ = ( a - b )³ + 3ab ( a - b )

And

a - b = √ { ( a + b )² - 4ab }

Here a = x and b = 1/x

Let's ist calculate x - 1/x

x - 1/x = √ { (2√3)² - 4 }

x - 1/x = √ { 8 }

x - 1/x = 2 √2

Now,

x³ - 1/x³ = ( 2√2 )³ + 3 ( 2√2 )

x³ - 1/x³ = 16√2 + 6√2

x³ - 1/x³ = √2 ( 16 + 6 )

x³ - 1/x³ = 22√2

Squaring both sides we get

( x³ - 1/x³ )² = ( 22√2 )²

(x³ - 1/x³)² = 968

______________________________

( √2 )³ = √2 × √2 × √2 = 2 √ 2

_____________________________

Have a nice day ahead.

Answer 2

Answer:

Maths AryaBhatta

Heya!!!

WE KNOW THAT

a³ - b³ = ( a - b )³ + 3ab ( a - b )

And

a - b = √ { ( a + b )² - 4ab }

Here a = x and b = 1/x

Let's ist calculate x - 1/x

x - 1/x = √ { (2√3)² - 4 }

x - 1/x = √ { 8 }

x - 1/x = 2 √2

Now,

x³ - 1/x³ = ( 2√2 )³ + 3 ( 2√2 )

x³ - 1/x³ = 16√2 + 6√2

x³ - 1/x³ = √2 ( 16 + 6 )

x³ - 1/x³ = 22√2

Squaring both sides we get

( x³ - 1/x³ )² = ( 22√2 )²

(x³ - 1/x³)² = 968

______________________________

( √2 )³ = √2 × √2 × √2 = 2 √ 2

_____________________________

Have a nice day ahead.

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