Question

The sum of all positive integral values of ‘a’ a∈[1, 500] for

which the equation [x]³ + x –a = 0 has solution is (where [⋅] denotes greatest integer)

• A. 469
• B. 625
• C. 812
• D. 904

Answer 1

Answer: (C)

812

Answer 2

∴ x = a – [x]³ ⇒ x∈I

⇒ a = x³ + x

∑a =

=$\left( \frac{7 \times 8}{2} \right)^{2} + \left( \frac{7 \times 8}{2} \right)$

=784 + 28 = 812