Question

If x^2+1/x=4, find the value of [x-1/x]

Answer 1

Your question needs a correction : x^2 + 1 / x^2 = 4

Answer:

± √2  ;  3 / 2

Step-by-step explanation:

Here,

⇒ x^2 + 1 / x^2 = 4

⇒ x^2 + 1 / x^2 - 2 = 4 - 2

⇒ x^2 + 1 / x^2 - 2( 1 ) = 2

⇒ x^2 + 1 / x^2 - 2( x * 1 / x ) = 2

⇒ ( x - 1 / x )^2 = 2                     { a^2 + b^2 - 2ab = ( a - b )^2 }

⇒ x - 1 / x = √2 or - √2

       

          If question is as same as given:

   (  x^2 + 1 ) / x = 4

   x^2  + 1 = 4x

   x^2 - 4x + 1 = 0

   ( x - 2 )^2 = 0

    x = 2

    Thus, x - 1 / x = 2 - 1 / 2 = ( 4 - 1 ) / 2 = 3 / 2