If X=a2 −b2 , Y=30 and a+b=15, then

Given: X = a^2 - b^2, Y = 30, and a + b = 15.

Step 1: Factor X using the difference of squares formula: X = (a - b)(a + b).

Step 2: Substitute the known value of (a + b) = 15 into the equation for X. This gives X = 15(a - b).

Step 3: Compare X and Y. We need to compare 15(a - b) with 30. Dividing both sides by 15, we compare (a - b) with 2.

Step 4: Analyze the condition a = b. If a = b, then (a - b) = 0. Thus, X = 15(0) = 0. Since Y = 30, X < Y and Y > X.

Step 5: Analyze the condition a > b. If a > b, then (a - b) > 0. However, X > Y only if (a - b) > 2. Therefore, a > b alone is not sufficient.

Conclusion: Options stating X < Y and Y > X when a = b are both valid. Thus, the option indicating more than one statement is correct is the right choice.