) Is this reasoning for finding the solutions of the equation √(22 – 1) = x correct? 1.1. √(22–1) = x is given; 22 − 1 = x2, obtained by squaring both sides of (1); x2 – 1 = 0, obtained by subtracting x2 from both sides of (2); (x − 1)(x + 1) = 0, obtained by factoring the left-hand side of x2 − 1; 1.5. x = 1 or x = −1, which follows because ab = 0 implies that a = 0 or b = 0
) Is this reasoning for finding the solutions of the equation √(22 – 1) = x correct? 1.1. √(22–1) = x is given; 22 − 1 = x2, obtained by squaring both sides of (1); x2 – 1 = 0, obtained by subtracting x2 from both sides of (2); (x − 1)(x + 1) = 0, obtained by factoring the left-hand side of x2 − 1; 1.5. x = 1 or x = −1, which follows because ab = 0 implies that a = 0 or b = 0
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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1) Is this reasoning for finding the solutions of the equation √(22 – 1) = x correct?
1.1. √(22–1) = x is given;
- 22 − 1 = x2, obtained by squaring both sides of (1);
- x2 – 1 = 0, obtained by subtracting x2 from both sides of (2);
- (x − 1)(x + 1) = 0, obtained by factoring the left-hand side of x2 − 1;
1.5. x = 1 or x = −1, which follows because ab = 0 implies that a = 0 or b = 0
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