2023 · Q29
If a, b and c are the sides of a triangle ABC, then √a + √b - √c is always :
Elementary MathematicsGeometry: Lines, Angles and Triangles
- ANegative
- BPositive
- CNon-negative
- DNon-positive
Explanation
√a + √b − √c > 0 is equivalent to a + b + 2√(ab) > c. By the triangle inequality a + b > c, and 2√(ab) > 0, so the inequality always holds. The expression is therefore always positive (B).