Question

If x?+1/x?=66 then find the value of x-1/x

Answer 1

x²+1/x²=66
or, (x-1/x)²+2(x)(1/x)=66
or, (x-1/x)²=66-2
or, (x-1/x)²=64
or, x-1/x=8 ; neglecting the negative sign.

Answer 2

Given that
[tex]x+ \frac{1}{x} = 66 [/tex]
Squaring on both sides

$(x+ \frac{1}{x})^2 = 4356$
$x^2+ \frac{1}{x^2} + 2.x.\frac{1}{x} = 4356$
$x^2+ \frac{1}{x^2} = 4354$

Now consider 
$x^2+ \frac{1}{x^2} - 2 = 4354 - 2$

$x^2+ \frac{1}{x^2} - 2.x.\frac{1}{x}<span> = 4352 </span>$


$(x- \frac{1}{x})^2 = 4352$

$x - \frac{1}{x} = 65.67$