Question

Determine two positive integers such as 5 less than two times the first number is the second number.
The sum of the second number and the square of the first is 115.

Answer 1

s = 2 f - 5

s + f^2 = 115

f^2 + 2 f - 5 = 115

f^2 + 2 f - 120 = 0

(f + 12)(f - 10) = 0

f - 10 = 0 ... f = 10

Answer 2

a = first number

b = second number

b = 2 a - 5

b + a ^ 2 = 115

2 a - 5 + a ^ 2 = 115

- 5 + a ^ 2 + 2 a = 115 Subtract 115 to both sides

- 5 + a ^ 2 + 2 a - 115 = 115 - 115

- 5 + a ^ 2 + 2 a - 115 = 0

Try to slove this equation.

The solutions are :

a = - 12 and a = 10

- 12 isn't positive integer so a = 10


b = b = 2 a - 5 = 2 * 10 - 5 = 20 -5 = 15