Question

if x+1/x =2 then x2+1/x2​

Answer 1

$hey \: dude \: here \: is \: your \: answer$

x+1/x=2

As we know that
(a+b)²=a²+b²+2ab

(x+1/x)²=(2)²

x²+1/x²+2=4

x²+1/x²=4-2

x²+1x²=2

hope this will help you

Answer 2

Answer:  The required value of the given expression is 2.

Step-by-step explanation:  We are given the following equality :

$x+\dfrac{1}{x}=2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the value of the following expression :

$x^2+\dfrac{1}{x^2}.$

We will be using the following formula :

$(a+b)^2=a^2+b^2+2ab.$

Squaring equation (i) on both sides, we have

$\left(x+\dfrac{1}{x}\right)^2=2^2\\\\\\\Rightarrow x^2+\left(\dfrac{1}{x}\right)^2+2\times x\times\dfrac{1}{x}=4\\\\\\\Rightarrow x^2+\dfrac{1}{x^2}+2=4\\\\\\\Rightarrow x^2+\dfrac{1}{x^2}=4-2\\\\\\\Rightarrow x^2+\dfrac{1}{x^2}=2.$

Thus, the required value of the given expression is 2.