Question

how to factorise xsqare+2+1/x square​

Answer 1

Answer:

Required factorised form of x^2 + 2 + 1 / x^2 is ( x + 1 / x )^2 .

Step-by-step explanation:

Method 1

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

= > x^2 + 2( x × 1 / x ) + 1 / x^2

Using a^2 + 2ab + b^2 = ( a + b )^2

= > ( x + 1 / x )^2

Method 2

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

= > x^2 + ( 1 + 1 ) + 1 / x^2

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

= > x^2 + 1 + ( x^2 + 1 ) / x^2

= > ( x^2 + 1 ) { 1 + 1 / x^2 }

= > ( x^2 + 1 ) { ( x^2 + 1 ) / x^2 }

= > ( x^2 + 1 )^2 / x^2

= > { ( x^2 + 1 ) / x }^2

= > ( x^2 / x + 1 / x )^2

= > ( x + 1 / x )^2

Hence the required factorised form of x^2 + 2 + 1 / x^2 is ( x + 1 / x )^2 .