Math, asked by hinatatum, 1 year ago

the value of (x+ 1/x)²

Answers

Answered by pinnaclewinner
15

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......

Answered by BrainlyIAS
73

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)

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