Absolute Value 1

From Homeworkwiki

Problem 1:Determine x when |x – 1| = 5

Solution: When x – 1 is positive |x – 1| = x – 1

Therefore, x – 1 = 5; Implies, x = 6

When x – 1 is negative |x - 1| = -(x - 1) [Since, |x| = -x when x is negative]

Hence, the equation becomes –(x - 1) = 5

Therefore, x – 1 = -5

Implies, x = -5 +1 = -4

Problem 2: Prove that |a|² = a²

Solution: If a is positive or 0, |a| = a

Therefore, |a|² = a²

If a is negative |a| = -a

Therefore, |a|² = ( -a) ² = a²

In both the cases, squaring we get |a|² = a²