Question

x + 1/x = 49 , find x - 1/x​

Answer 1

As per the data given in the question,

We have to determine the value of $x -\frac{1}{x}$

As per question,

It is given that,

The value of $x +\frac{1}{x} = 49$

So, solving the expression,

We will get it as,

$x +\frac{1}{x}=49\\=>\frac{x^2+1}{x} = 49\\=>x^2+1=49x\\=>x^2-49x+1=0$

Now comparing it with standard equation of quadratic equation,

$ax^2+bx+c =0$

We will get it as,

$a = 1, b = -49, c = 1$

So, value of quadratic equation will be,

$\frac{-b+{\sqrt{b^2-4ac}}}{2a}\\=\frac{-(-49)+{\sqrt{(-49)^2-4\times 1\times 1}}}{2\times 1}\\=\frac{49+{\sqrt{2401-4}}}{2}\\=\frac{49+{\sqrt{2397}}}{2}$

As we know that,

${\sqrt{2397}} = 48.9591 \approx 48.96$

So, value of roots will be $\frac{49+48.96}{2} =48.98$

Hence, value of required expression will be,

$x-\frac{1}{x} = 48.96-\frac{1}{48.98} =48.96 - 0.02 =48.94$