99 Percentile Qs Bank for JEE MainMathematicsQuadratic Equation
Let D = a 2 + b 2 + c 2 , where a ,   b being consecutive integers and c = a b , then D is
Options
- Aalways an even integer.
- Balways an odd integer.
- Calways irrational.
- Dcan't be discussed.
Correct answer
B. always an odd integer.
Step-by-step solution
We have, D = a 2 + b 2 + c 2 Since, a and b are consecutive integers therefore, b = a + 1 and c = a b = a a + 1 . Then D = a 2 + b 2 + c 2 = a 2 + a + 1 2 + a 2 a + 1 2 = a 2 1 + a + 1 2 + a + 1 2 = a 2 a 2 + 2 a + 2 + a 2 + 2 a + 1 = a 4 + 2 a 3 + 3 a 2 + 2 a + 1 = a 2 + a + 1 2 ∴   D = a a + 1 + 1 = an odd integer.