Question

the value of (x+ 1/x)²

Answer 1

Answer:

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

${(x + y)}^{2} = {x}^{2} + {y }^{2} + 2xy$

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

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

Step-by-step explanation:

Hope it helps you out......

Answer 2

Answer

• x² + ¹/ₓ² + 2

Given

$\bullet \;\; \rm \bigg(x+\dfrac{1}{x}\bigg)^2$

To Find

• Value of the given

Formula

$\bullet \;\; \rm (a+b)^2=a^2+b^2+2ab$

Solution

$\rm Compare\ given\ with\ (a+b)^2\ ,we\ get\ ,\\\\\implies \rm a=x\ ,b=\dfrac{1}{x}$

So ,

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

More Info

$\bullet \;\; \rm (a-b)^2=a^2+b^2-2ab\\\\\bullet \;\; \rm a^2-b^2=(a+b)(a-b)\\\\\bullet \;\; \rm (a+b)^3=a^3+b^3+3ab(a+b)\\\\\bullet \;\; \rm (a-b)^3=a^3-b^3-3ab(a-b)$