The difference between two positive integers is 4. if the smaller is added to the square of the larger, the sum is 68. find the integers.

Two positive integers x and y

x - y = 4

x² + y = 68

x and y

Add the two equations together.

... (x - y) + (x² + y) = (4) + (68)

... x² + x = 72

Rearrange to standard form and factor.

... x² + x - 72 = 0

... (x + 9)(x - 8) = 0

Use the zero product rule to find the solutions. That rule says the product is zero when one or more factors is zero.

... x + 9 = 0 ⇒ x = -9

... x - 8 = 0 ⇒ x = 8 . . . . . . the positive solution

Then we can find y from

... 8 - y = 4

... y = 4 . . . . . . . add y-4 to the equation

The two positive integers are 8 and 4.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: