Question

If x+1/x=4 then prove this X2+1/X2=14

Answer 1

Answer:

Yes, it is proved.

Step-by-step explanation:

Here we have mentioned proving the value of $x^{2} + \frac{1}{x^{2} }$ to be 14 and we have been given the value of $x + \frac{1}{x} = 4$

We will use the following identity for finding this as below:

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

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

$x^{2}+ \frac{1}{x^{2} }= (4 )^{2} - 2$

            = 16 - 2

            = 14

Hence proved.