Question

Expand (X+1/X) power 2​

Answer 1

Answer:

(x+1/x)^2

=x^2+1/x^2+2×x×1/x

=x^2+1/x^2+2

Step-by-step explanation:

Since,by using (a+b)^2 identity,we get x2+1/x2+2x1/x

.As x and 1/x get cut we get 2 only hence,

x^2+1/x^2+2

I HOPE IT HELPS......

Answer 2

We have to expand the following expression :-

${(x + \dfrac{1}{x} )}^{2}$

Now we know that :-

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

therefore now :-

$\implies{(x + \dfrac{1}{x} )}^{2} = {x}^{2} + {(\dfrac{1}{x} )}^{2} + 2.x.(\dfrac{1}{x})$

$\implies{(x + \dfrac{1}{x} )}^{2} = {x}^{2} + {(\dfrac{1}{x} )}^{2} + 2.1.\dfrac{1}{1}$

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

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

Answer :

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

_______________________

$\large\bf\green{Learn\:More}$

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

$\implies{(a-b)^2 = a^2 + b^2 - 2ab}$

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

______________________