Math Problem Statement

solve

Which expression is equal to |a - 2 - √(a - 1)^2| for a < 0?

Solution

The expression a2(a1)2\left| a - 2 - \sqrt{(a - 1)^2} \right| for a<0a < 0 simplifies to:

a+a1+2\left| -a + \left| a - 1 \right| + 2 \right|

Would you like a more detailed breakdown of this solution?

Here are 5 related questions that could expand your understanding:

  1. How does the absolute value function affect the result for different values of aa?
  2. What happens if a0a \geq 0? How would the expression simplify in that case?
  3. What is the geometric interpretation of absolute values and square roots in this context?
  4. How does the expression change if (a1)2\sqrt{(a - 1)^2} is expanded explicitly?
  5. How do we handle expressions inside absolute value functions when solving inequalities?

Tip: When simplifying expressions with square roots and absolute values, consider the sign of the variable inside the square root.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value
Square Roots

Formulas

Absolute value function: |x|
Square root simplification: √(x^2) = |x|

Theorems

Properties of absolute values
Simplification of square roots

Suitable Grade Level

Grades 9-12