Question

(x^2+1/x^2)-4(x+1/x)+6 please factorise

Answer 1

Answer:

(√x - 1/√x)^4

Step-by-step explanation:

use a^2 b^2 = (a+b)^2 - 2ab

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

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

now put this in above ,

= [x+1/x)^2 - 2] - 4(x+1/x)+6

= (x+1/x)^2 - 4(x+1/x) + 4

now put (x+1/x) = y

then y^2 - 4y + 4

= (y - 2)(y - 2)

i.e, (x+1/x -2)(x+1/x -2)

= [(x-1)^2/x][(x-1)^2/x]

= (x-1)^4/x^2

or (√x - 1/√x)^4