Question

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

u =

x

4(x +1)
x +1

(x + 1)2
Select the solution(s) of the original equation.

x = 1 + sqrt 2

x = 2 + sqrt 2

x = 3 + sqrt 2
x = 1 - sqrt 2

x = 2 - sqrt 2

x = 3 - sqrt 2

Answer 1

Answer: 1st - x = 1 + √2 & 4th- x= 1 - √2

Explanation:

Answer 2

For this case we have to:

Let
`u = x + 1`

So:

`u ^ 2-4u + 2 = 0`

We have the solution will be given by:

`u = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}`

Where:

`a = 1\\b = -4\\c = 2`

Substituting:

`u = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (1) (2)}} {2 (1)}\\u = \frac {4 \pm \sqrt {16-8}} {2}\\u = \frac {4 \pm \sqrt {8}} {2}\\u = \frac {4 \pm \sqrt {2 ^ 2 * 2}} {2}\\u = \frac {4 \pm2 \sqrt {2}} {2}`

The solutions are:

`u_ {1} = \frac {4 + 2 \sqrt {2}} {2} = 2 + \sqrt {2}\\u_ {2} = \frac {4-2 \sqrt {2}} {2} = 2- \sqrt {2}`

Returning the change:

`2+ \sqrt {2} = x_ {1} +1\\x_ {1} = 1 + \sqrt {2}\\2- \sqrt {2} = x_ {2} +1\\x_ {2} = 1- \sqrt {2}`

Answer:

`x_ {1} = 1 + \sqrt {2}\\x_ {2} = 1- \sqrt {2}`