Question

If x^2 + 1/x^2
=2, evaluate x.​

Answer 1

Answer:

X^2 +1/X^2 =2

or, X^2 + (1/X)^2 =2

or,( X +1/X)^2 -2 =2

or, X + 1/X =2 -(1)

again,

X^2 +1/X^2 =2

or,X -1/X =0 -(2)

by method of elimination,

2X = 2

or, X =1

& 1/X = 1

Answer 2

Answer:

To find -  x

Solution -  x²+1/x²=2

⇒ x^4 +1\x²=2                             (by taking lcm)

   x^4 +1=2x²

   x^4 - 2x² + 1=0

⇒ x^4 - x² - x² + 1=0                   (middle term splitting)

    x²(x²-1)-1(x²-1) = 0

   (x²-1) (x²-1) = 0

    x²-1=0 , x²-1=0                       (equating both factors with zero)

    x²=1 , x²=1

    x=√1

⇒x = 1                                         (square root of 1 is 1)