Question

Find the roots of the following equations : (i) `x+1/x=3, x!=0` (ii) `1/x-1/(x-2)=3,x!=0,2`

Answer 1

(i) `x+ 1/x = 3`
`x^2 + 1 = 3x`
`x^2 - 3x + 1 = 0`
`D= b^2 - 4ac`
`= (-3)^2 - 4(1)(1)`
`= 9-4 =5`
roots are `(-b+- sqrtD)/(2a)`
`= (3+ sqrt 5)/2 & (3 - sqrt5)/2`
answer (ii) `1/x - 1/(x-2) = 3`
`x-2 -x= 3(x^2 - 2x)`
`-2 = 3x^2 - 6x`
`3x^2 - 6x + 2 = 0`
`D= b^2 - 4ac`
`= (-6)^2 - 4(3)(2) = 36 - 24 = 12`
roots are `(6+ sqrt12)/6 & (6 - sqrt12)/6`
answer