1/x to the second power + 1/2=1/2xto the second power

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

Clearly,

1/x^2 + 1/2 - (1/2)x^2 = 0

Take LCM , 2x^2 and solve

( 2 + x^2 - x^4)/2x^2 = 0

Taking denominotor to other side, hence it will geet multiplied by 0 hence will become 0.

2 + x ^2 - x^4 = 0

x ^4 - x ^2 - 2 = 0

x ^4 - 2 x ^2 + x ^2 - 2 = 0

x ^2 ( x^2 - 2 ) + 1 ( x ^2 - 2 ) = 0

( x ^2 + 1 ) ( x^2 - 2 ) = 0

x ^2 + 1 = 0 or x ^- 2 = 0

Ignoring 1st case as it will give completx roots.

x^2 - 2 = 0

x^2 = 2

x = (+ root 2 ) and ( - root 2)

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