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

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter9: Systems Of Linear Equations

Section9.7: Puzzle Problems

Problem 8OE

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