Question

if(x+1/x)=6,find the values of 1.(x+1/×) 2. (x^2 - 1/x^2)​

Answer 1

$\: \: \sf \: {( x + \frac{1}{x}) }^{2}$

As we know

$\: \: \sf \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

From this identity now we will put the value which is given

$\: \: \sf \: (x + \frac{1}{x} ) = 6$

Now put on this value and find (x+1/x)^2

$\: \: \sf \: {(x + \frac{1}{x}) }^{2} = {x}^{2} + { \frac{1}{ {x}^{2} } } + 2x \frac{1}{x} \\ \\ \: \: \sf \: = {(x + \frac{1}{x} )}^{2} + 2 \\ \\ \: \: \sf \: = {(6)}^{2} + 2 \\ \\ \: \: \sf \: = 36 + 2 \\ \\ \: \: \sf = 38$

Hence,(x+1x)^2 = 38.