32.9k views
3 votes
Solve (x + 1)2 – 4(x + 1) + 2 = 0 using substitution. u =

User Menjaraz
by
8.8k points

2 Answers

7 votes


(x+1)^2-4(x+1)+2=0\qquad\text{substitute}\ u=x+1\\\\u^2-4u+2=0\qquad\text{add 2 to both sides}\\\\u^2-4u+4=2\\\\u^2-2(u)(2)+2^2=2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(u-2)^2=2\iff u-2=\pm\sqrt2\qquad\text{add 2 to both sides}\\\\u=2-\sqrt2\ \vee\ u=2+\sqrt2\\\\\text{Therefore}\\\\x+1=2-\sqrt2\ \vee\ x+1=2+\sqrt2\qquad\text{subtract 1 from both sides}\\\\\boxed{x=1-\sqrt2\ or\ x=1+\sqrt2}

User Patrik Stas
by
8.9k points
1 vote

Answer:

c. x+1 on edg

Explanation:

the solutions to the original question are

a. x= 1+
√(2)

d. x= 1-
√(2)

User Oscarm
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories