What are the two consecutive numbers with a product of 7310?

Answer 1

Let the number be 'n' & 'n+1' ; consecutive.

Hence

n(n+1) = 7310 ( product)

n^(2) + n = 7310

Complete the Square

( n + 1/2)^(2) - (1/2)^(2) = 7310

( n + 1/2)^2 - 1/4 = 7310

(n + 1/2)^(2) = 7310.25

Square root both sides

n+ 1/2 = +/- 85.5 (NB 1/2 = 0.5)

n = 85.5 - 0.5 = 85

Hence n + 1 = 86

Verification 85 X 86 = 7310

Answer 2

They are 85 and 86.

Find sqrt(7310) = 85.499.

Round the answer up and down to integers.