The sum of the squares of two consecutive odd numbers is 970. find type integers

21, 23 and -21, 23

Step-by-step explanation:

The difference between two consecutive odd numbers is 2.

Let the smaller number be x. Then, the larger number is x + 2.

Now add their squares and set it equal to 970. Then  solve for x.

smaller number: x

larger number: x + 2

sum of the squares of the two numbers: x^2 + (x + 2)^2

equation: x^2 + (x + 2)^2 = 970

Solution of the equation:

x^2 + (x + 2)^2 = 970

Expand the square of the binomial:

x^2 + x^2 + 4x + 4 = 970

Combine like terms on the left side:

2x^2 + 4x + 4 = 970

Subtract 970 from both sides:

2x^2 + 4x - 966 = 0

Divide both sides by 2:

x^2 + 2x - 483 = 0

Now we need to factor the binomial. We need two number whose sum is 2 and whose product is -483. Look at 483. It is not divisible by 2, but it is divisible by 3.

483/3 = 161

161 is divisible by 7.

161/7 = 23

23 is prime, so the prime factorization of 483 is

483 = 3 * 7 * 23

Notice that 3 * 7 = 21, so

483 = 21 * 23

Use -21 and 23:

-21 + 23 = 2

-21 * 23 = -483

x^2 + 2x - 483 factors into (x - 21)(x + 23)

Now we continue solving the equation.

x^2 + 2x - 483 = 0

(x - 21)(x + 23) = 0

x - 21 = 0 or x + 23 = 0

x = 21 or x = -23

We let x equal the smaller of the two integers, so now we add 2 to find the second integer.

x = 21; x + 2 = 23

x = -23; x + 2 = -21

There are two sets of consecutive odd numbers that satisfy this problem.

21, 23

-23, -21

The problem did not state positive or negative consecutive odd numbers, so both solutions are valid.

where did you get them? if you picked from the grass, is is probably poisonous.

step-by-step explanation: