Prove that equation x2 + 2x +1 + y² = 0 has only one solution: x = -1 and y = 0. Individual steps of a correct proof are given below, you only need to choose the correct ordering of these steps. Proof: (1) In the second case, when y + 0, rewrite this equation as a2 + 2x + 1 + y² = (x + 1)? + y?. (2) Summarizing, we showed that in the first case the only solution is æ = –1 and y = 0, and in the second case there is no solution --- completing the proof. (3) We will consider two cases: when y O and when y + 0. (4) Since (x + 1)² > 0 and y² > 0, we obtain that a2 + 2x + 1+ y? = (x + 1)² + y² > 0, that is the equation does not have a solution in this case. (5) In the first case, for y = 0, this is a quadratic equation x2 + 2x +1 = 0 and its only root is x = -1. QED From the list below, select an ordering of these statements that will form a correct proof: O 1-3-4-5-2 O 3-5-1-4-2 O 4-1-5-2-3 O 3-2-5-4-1 O 3-1-5-4-2
Prove that equation x2 + 2x +1 + y² = 0 has only one solution: x = -1 and y = 0. Individual steps of a correct proof are given below, you only need to choose the correct ordering of these steps. Proof: (1) In the second case, when y + 0, rewrite this equation as a2 + 2x + 1 + y² = (x + 1)? + y?. (2) Summarizing, we showed that in the first case the only solution is æ = –1 and y = 0, and in the second case there is no solution --- completing the proof. (3) We will consider two cases: when y O and when y + 0. (4) Since (x + 1)² > 0 and y² > 0, we obtain that a2 + 2x + 1+ y? = (x + 1)² + y² > 0, that is the equation does not have a solution in this case. (5) In the first case, for y = 0, this is a quadratic equation x2 + 2x +1 = 0 and its only root is x = -1. QED From the list below, select an ordering of these statements that will form a correct proof: O 1-3-4-5-2 O 3-5-1-4-2 O 4-1-5-2-3 O 3-2-5-4-1 O 3-1-5-4-2
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Transcribed Image Text:Prove that equation æ2 + 2x +1 + y? = 0 has only one solution: a = -1 and y = 0.
Individual steps of a correct proof are given below, you only need to choose the correct
ordering of these steps.
Proof:
(1) In the second case, when y + 0, rewrite this equation as x² + 2x + 1+ y² = (x +
1)2 + y?.
(2) Summarizing, we showed that in the first case the only solution is x = -1 and y = 0, and
in the second case there is no solution --- completing the proof.
(3) We will consider two cases: when y = 0 and when y + 0.
(4) Since (x + 1)? > 0 and y? > 0, we obtain that æ? + 2x +1+ y? = (x + 1)? + y?
0, that is the equation does not have a solution in this case.
(5) In the first case, for y = 0, this is a quadratic equation x2 + 2x +1 = 0 and its only root is
x = -1.
QED
From the list below, select an ordering of these statements that will form a correct proof:
O 1-3-4-5-2
O 3-5-1-4-2
O 4-1-5-2-3
O 3-2-5-4-1
O 3-1-5-4-2
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
