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Zolol [24]
3 years ago
15

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

Mathematics
2 answers:
lara31 [8.8K]3 years ago
5 0

Answer: c) x+1

Step-by-step explanation:

trust me on edg

solniwko [45]3 years ago
3 0

For this case we have to:

Letu = 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}

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