Determine the two positive real numbers whose ratio is , and the square of the small number exceeds 7 times the great number by 560.
Use and , the ratio and the relationship between and to write two equations. Then solve.
The ratio between two integers and is
The square of exceeds 7 times by 560
Factor to solve for possible values of
Therefore, the smaller number is 28.
Substitute into to find
Therefore, the numbers are 28 and 32.