Question

Solve (x + 1)2 - 4(x + 1) + 2 = 0 using substitution.

U=


х

4(x +1)

O x +1

(x + 1)2

Answer 1

Answer: x+4

Step-by-step explanation: part one- x+4

Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4

Answer 2

Explanation:

We are given the equation
`(x+1)^2-4(x+1)+2=0`. Consider the substitution u = (x+1). Then the equation turns out to be
`u^2-4u+2=0`

Recall that given a second degree polynomial of the form
`ax^2+bx+c =0` then its solutions are given by the expression

`x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}`

In our case, a = 1, b = -4 and c =2. Then the solutions are

`u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}`

`u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}`

We have that x = u-1. So the original solutions are

`x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}`

`x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}`