Question

if x=√7+4√3 then find the value of x+1/x​

Answer 1

The value of x + 1/x = $2\sqrt{7}$.

• The value of x is given as √7+4√3 .
• We have to find the value of x+1/x.
• We find the reciprocal of x as,

1/x = $\frac{1}{\sqrt{7}+4\sqrt{3}}$

Now we multiply the reciprocal with the conjugate and simplify the reciprocal of x,

Conjugate of √7+4√3 is √7-4√3.

Multiplying numerator and denominator with the reciprocal, we get

1/x = $\frac{1}{\sqrt{7}+4\sqrt{3}}$ × $\frac{\sqrt{7}-4\sqrt{3}}{\sqrt{7}-4\sqrt{3}}$

1/x = $\frac{\sqrt{7}-4\sqrt{3}}{(\sqrt{7})^2 - (4\sqrt{3} )^2}$

1/x = $\frac{\sqrt{7}-4\sqrt{3}}{49 - 48}$

1/x = $\sqrt{7}-4\sqrt{3}$.

• Now we have to find the value of x+1/x,

x + 1/x = $\sqrt{7}+4\sqrt{3}$ + $\sqrt{7}-4\sqrt{3}$

x + 1/x = $2\sqrt{7}$