Question

Given: \( a \) and \( b \) are positive integers and \( a>b \). The median of a set consisting of 5 terms: \( a^2, ab, b^2, (a - b)^2 \) and \( (a + b)^2 \) is \( ab \).

• A. Always
• B. Sometimes
• C. Never
  % Correct answer
• D.
• E.

Hint:

When dealing with ordered sets of terms, always ensure to compare each term's magnitude to find the correct median.

Answer 1

The Correct Option is A

The set consists of five terms: \( a^2, ab, b^2, (a - b)^2, (a + b)^2 \). Arranging the terms in increasing order of magnitude, we find that \( ab \) is always the middle term. Therefore, the median is always \( ab \), regardless of the specific values of \( a \) and \( b \). Hence, the correct answer is "Always".