Question

How do you solve `1/x + 1 = x/2`?

Answer 1

Solns. are `x=1+-sqrt3.`

Explanation:

Given Eqn. `:1/x+1=x/2`

Multiplying throughout by `2x`, eqn. becomes, `2+2x=x^2`
`:. x^2-2x=2.`

Adding `1` in both sides, `x^2-2x+1=2+1,` or, `(x-1)^2=3`

`:. x-1=+-sqrt3`, i.e., `x=1+-sqrt3,` are the reqd. solns.