Question

if x = √3 - 2, find the value of (x + 1 / x )^3
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Answer 1

Answer:

-64

Step-by-step explanation:

⇒ x = √3 - 2

⇒ 1 / x = 1 / ( √3 - 2 )

Multiplying and dividing RHS by √3 + 2

⇒ 1 / x =  ( √3 + 2 ) / [ ( √3 - 2 )( √3 + 2 )

⇒ 1 / x = ( √3 + 2 ) / [ ( √3 )^2 - ( 2 )^2 ]      { ( a + b )( a - b ) = a^2 - b^2 }

⇒ 1 / x = ( √3 + 2 ) / [ 3 - 4 ]

⇒ 1 / x = ( √3 + 2 ) / ( - 1 )

⇒ 1 / x = - √3 - 2

Therefore,

⇒ x + 1 / x = ( √3 - 2 ) + ( - √3 - 2 )

⇒ x + 1 / x = √3 - 2 - √3 - 2

⇒ x + 1 / x = - 4

Thus,

⇒( x + 1 / x )^3 = ( - 4 )^3 = - 64

Answer 2

Answer:-24√3

Given

X=√3-2

To find

(x$\frac{1}{x}$)³

Solution

We know that

(x+$\frac{1}{x}$)³=x³+$\frac{1}{x}$³+3x×$\frac{1}{x}$(x+$\frac{1}{x}$)

Now finding for

$\frac{1}{x}$

X=√3-2

$\frac{1}{x}$= $\sf{\dfrac{1}}{\sqrt{3-2}}$(Rationalising)

=>$\frac{1}{x}$= $\sf{\dfrac{\sqrt{3}}{1}}$×$\sf{\dfrac{\sqrt{3}}{1}}$

$\frac{1}{x}$=√3+2

Putting the values in

(x$\frac{1}{x}$)³

=>(x$\frac{1}{x}$)³=(√3-2+√3+2)³

=(2√3)³

=24√3