Question

Help please and show the steps. thanks!​

Answer 1

`{x}^(4) - 5 {x}^(3 ) + 7 {x}^(2) - 5x + 6 = 0 \\ - 5x( {x}^(2) + 1) + ( {x}^(2) )^(2) + 7 {x}^(2) + 6 = 0 \\ {x}^(2) = u \\ - 5x( {u} + 1) + (u^(2) + 7 u + 6) =0`

`u^(2) + 7 u + 6=0 \\ u_1 = - 1 \\ u_2= - 6 \\ (u-u_1)(u-u_2) \\ u^(2) + 7 u + 6 = (u + 1)(u + 6)`

`- 5x( {u} + 1) + u^(2) + 7 u + 6 = 0 \\ - 5x(u + 1) + (u + 1)(u + 6) = 0 \\ u = {x}^(2) \\ - 5x( {x}^(2) + 1) + ( {x}^(2) + 1)( {x}^(2) + 6) =0`

`( {x}^(2) + 1)( {x}^(2) - 5x + 6) = 0`

Now we have 2 equations

`{x}^(2) + 1 = 0 \\ {x}^(2) = - 1 \\ x_1 = i \\ x_2 = - i`

`{x}^(2) - 5x + 6 = 0 \\ D = {( - 5)}^(2) - 4 * 6 = 1 = {1}^(2) \\ x_3= (5 + 1)/(2) = 3 \\ x_4 = (5 - 1)/(2) = 2`

`Answer:x_1=-i, x_2=i, x_3=2, \\ x_4=3`