2020 · Q5
If I = a² + b² + c², where a and b are consecutive integers and c = ab, then I is
Elementary MathematicsNumber System
- Aan even number and it is not a square of an integer
- Ban odd number and it is not a square of an integer
- Csquare of an even integer
- Dsquare of an odd integer
Explanation
Let b = a+1. Then I = a^2+(a+1)^2+a^2(a+1)^2 = (ab)^2+2ab+1 = (ab+1)^2, a perfect square. Since a and a+1 are consecutive, ab is even, so ab+1 is odd. Thus I is the square of an odd integer - option (D).