Question

x+1/x=2 but x²+1/x²=??​

Answer 1

Answer:

Your answer is in attachement

Answer 2

Answer:

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

Step-by-step explanation:

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

we use following formula

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

now, by squaring both side in equation (1) we get

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

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