Question

If x=2+√3 then x+1/x is​

Answer 1

GIVEN:-

• if $\rm{ x = 2 + \sqrt{3}}$

TO FIND :-

• The Value of $\rm{x + \dfrac{1}{x}}$

HOW TO SOLVE :-

• we will Rationalise the Denominator form.

Now,

$\implies\rm{ x = 2 + \sqrt{3}}$

$\implies\rm{ \dfrac{1}{x} = \dfrac{1}{2 + \sqrt{3}}}$

$\implies\rm{ \dfrac{1}{x} = \dfrac{1}{2 + \sqrt{3}} \times{\dfrac{2 - \sqrt{3}}{2 - \sqrt{3}}}}$

$\implies\rm{\dfrac{2 - \sqrt{3}}{(2)^2 - (\sqrt{3})^2}}$

$\implies\rm{ 2 - \sqrt{3}}$.

Therefore,

$\implies\rm{ x + \dfrac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3}}$

$\implies\rm{ x + \dfrac{1}{x} = 4}$.

Hence, The Value of x + 1/x is 4.

SOME ALGEBRAIC IDENTITIES.

• (a+b)² = a² + 2ab + b²

• (a-b)² = a² - 2ab + b²

• a³ + b³ = (a+b) (a²-ab+b²).

• a³ - b³ = (a-b) (a²+ab+b²).

Answer 2

Step-by-step explanation:

X=2√3

1/x=1/(2+√3)*(2-√3)/(2-√3)

1/x=(2-√3)/(4-3)

[(a-b)(a+b)=(√a-√b)]

1/x=(2-√3)

now,

x+1/x=(2+√3)+(2-√3)

x+1/x=2+2+√3-√3

x+1/x=4