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12. Is this reasoning for finding the solutions of the equation V 2x – 1 = X correct? (1) 2x - 1 = X is given; %3D (2) 2x (1); - 1 : x ,obtained by squaring both sides of 2 X - 1 = 0, obtained by subtracting x from both (3) sides of (2); (4) (x – 1) (x + 1) = 0, obtained by factoring the %3D 2 left-hand side of x - 1; -%3B (5) implies that a = 0 or b = 0. X = 1 or X = -1, which follows because ab = 0 %3D

12. Is this reasoning for finding the solutions of the equation V 2x – 1 = X correct? (1) 2x - 1 = X is given; %3D (2) 2x (1); - 1 : x ,obtained by squaring both sides of 2 X - 1 = 0, obtained by subtracting x from both (3) sides of (2); (4) (x – 1) (x + 1) = 0, obtained by factoring the %3D 2 left-hand side of x - 1; -%3B (5) implies that a = 0 or b = 0. X = 1 or X = -1, which follows because ab = 0 %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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12. Is this reasoning for finding the solutions of the equation V 2x – 1 = X correct? (1) 2x - 1 = x is given; %3D 2x – 1 = x ,obtained by squaring both sides of (1); X - 1 = 0, obtained by subtracting x from both (3) sides of (2); (4) (x – 1) (x + 1) = 0, obtained by factoring the %3D 2 left-hand side of x- 1; -%3B (5) X = 1 or X = -1, which follows because ab = 0 %3D implies that a = 0 or b = 0.
Transcribed Image Text:12. Is this reasoning for finding the solutions of the equation V 2x – 1 = X correct? (1) 2x - 1 = x is given; %3D 2x – 1 = x ,obtained by squaring both sides of (1); X - 1 = 0, obtained by subtracting x from both (3) sides of (2); (4) (x – 1) (x + 1) = 0, obtained by factoring the %3D 2 left-hand side of x- 1; -%3B (5) X = 1 or X = -1, which follows because ab = 0 %3D implies that a = 0 or b = 0.
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