The difference between two positive integers is2. If the smaller is added to the square of the larger the sum is 40. Find the integers

4 and 6

Step-by-step explanation:

first you must write your let statements

let x = smaller integer

let y = bigger integer

y - x = 2

x + y^2 = 40

then you use substition to find your anaswer

x = y - 2

y - 2 + y^2 = 40

y^2 + y - 42 = 0

then find the numbers that add up to 1 and multiply to -42

-6 and 7

y^2 + 7y - 6y - 42

y(y + 7) - 6(y + 7)

(y - 6)(y + 7)

set both sides equal to 0

y = 6, -7

y must be positive so it is 6

then plug y into one of the equations to get your answer

6 - x = 2

x = 4

your answer is 4 and 6

45

step-by-step explanation: