two consecutive natural numbers are such that the square of the larger exceeds three times the lower 57. Find the greatest number.

(x+1)^2=3x+57.

x^2+2x+1-3x-57=0.

x^2-x-56=0.

(x-8)(x+7)=0.

x=8, -7.

Ignore negavtive number.

The consecutive natural numbers are 8,9.