Question

one positive integer is 4 less than twice another. the sum of their squares is 901. find the integers.

smaller integer =
larger integer =

Explanation:

Define variables and set up equations

Let the first positive integer be \(x\).
The other positive integer is 4 less than twice \(x\), which is \(2x - 4\).
The sum of their squares is 901:

$$x^2 + (2x - 4)^2 = 901$$

Expand the quadratic equation

Using the Square of a Binomial Difference knowledge point

$$
LATEXBLOCK0
$$

Write in standard form

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK1
$$

Solve for x using the quadratic formula

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK2
$$

Since \(x\) must be a positive integer:

$$
LATEXBLOCK3
$$

Find the two integers

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK4
$$

Comparing the values, the smaller integer is 15 and the larger integer is 26.

Answer:

One positive integer is 4 less than twice another. The sum of their squares is 901. Find the integers.

smaller integer = <blank>15</blank>

larger integer = <blank>26</blank>