Question

if x=2+root 3 = 27, find x-1/x​

Answer 1

Step-by-step explanation:

The value of \bold{x-\frac{1}{x} \text { is } 5}.

To find:

Find x-\frac{1}{x}

Solution:

Given: x^{2}+\frac{1}{x^{2}}=27

We know that (a-b)^{2}=a^{2}+b^{2}-2 a b

Putting a=x, b=\frac{1}{x}

\left(x-\frac{1}{x}\right)^{2}

=x^{2}+\frac{1}{x^{2}}-2 \times x \times \frac{1}{x}

=x^{2}+\frac{1}{x^{2}}-2

=27-2\ (Given\ that\ x^{2}+\frac{1}{x^{2}}=27)

=25

Hence, \left(x-\frac{1}{x}\right)^{2}=25

\left(x-\frac{1}{x}\right)^{2}=(5)^{2}

Taking square root of both sides, we get

\bold{x-\frac{1}{x}=5}