Which of the following statements is true for all positive integers a and b, where a ≠ ba?
Show answer & explanation
Correct answer: C
Explanation
Among the options provided in the image, the condition "a ≠ b" stated in the question is actually not necessary for this specific problem. The correct statement is to be selected based solely on algebraic identities.
Check the options:
A) √a + √b = √(a + b) ✗ (Generally incorrect)
B) √a − √b = √(a − b) ✗ (Generally incorrect)
C) (√a + √b)² = a + b + 2√ab ✓ (Always true)
D) (√a + √b)² = a + b − 2√ab ✗ (This is the expansion of (√a − √b)²)
(√a + √b)² = a + b + 2√ab