Question

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

Answer 1

Solution

Given :-

• x = (2 - √4)

Find :-

• Value of ( x + 1/x)³

Explanation

Using Formula

★ ( a + b)³ = a³ + b³ + 3a²b + 3ab²

First Calculate 1/x

==> 1/x

keep Value of x

==> 1/(2-√3)

Rationalize denominator

==> (2+√3)/(2-√3)(2+√3)

==> (2+√3)/(2²-√3²)

==> (2+√3)/(4-3)

==> (2+√3)

Now, Calculate ( x + 1/x)

==> ( x + 1/x)

keep Value of x

==> [ (2-√3) + (2+√3)]

==> 4

Now, Calculate ( x + 1/x)³

==> ( x + 1/x)³

Keep Value of ( x + 1/x)

==> (4)³

==> 64

Hence

• Value of ( x + 1/x)³ be = 64

________________

Answer 2

$\huge{\underline{\sf{\blue{ANSWER}}}}$

GIVEN:-

• If x = $2-\sqrt{3}$

TO FIND:-

• The value of $x+\frac{1}{x^3}$

EXPLANATION-:

• if we have to find the value of $x+\frac{1}{x^3}$ then we have to find the value of $\frac{1}{x}$

FORMULA USED:-

• Rationalising.

$\implies{x=2-\sqrt{3}}$

$\implies{\frac{1}{x}=\frac{1}{2-\sqrt{3}}}$

$\implies{\frac{1}{2-\sqrt{3}}×\frac{2+\sqrt{3}}{2+\sqrt{3}}}$

• After rationalising it we get $\frac{1}{x}$ $2+\sqrt{3}$

Now,

Put the values..

$\implies{x+\frac{1}{x}}$

$\implies{2-\sqrt{3}+2+\sqrt{3}}$

$\implies{4}$

The value of $\huge{x+\frac{1}{x}\:is\:4}$

Atq.

$\implies\huge{(x+\frac{1}{x})^3=4^3}$

$\implies\huge{x^3+\frac{1}{x^3}=64}$

●●SOME EXTRA INFORMATION●●

$(a+b)^2=a^2+b^2+2ab$

$(a-b)^2=a^2-2ab+b^2$

$a^3+b^3=(a+b) (a^2-ab+b^2)$