## The sum of the squares of two consecutive odd integers is 1570. find the integers

Question

The sum of the squares of two consecutive odd integers is 1570. find the integers

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1 month 2021-08-14T18:05:46+00:00 2 Answers 0 views 0

## Answers ( )

1. Answer:

Step-by-step explanation:

Let’s look at a few examples of two consecutive odd integers.

1, 3

11, 13

55, 57

Notice that the larger integer is always 2 more than the smaller one.

If you let the smaller one be x, then the larger one is x + 2.

Now we square the two numbers.

The square of x is x^2.

The square of x + 2 is (x + 2)^2.

Now we add those two squares and set equal to 1570.

x^2 + (x + 2)^2 = 1570

x^2 + x^2 + 4x + 4 = 1570

2x^2 + 4x + 4 = 1570

2x^2 + 4x – 1566 = 0

x^2 + 2x – 783 = 0

783 is 290 * 27

(x – 27)(x + 29) = 0

x – 27 = 0 or x + 29 = 0

x = 27 or x = -29

Remember that x is the smaller of the two integers.

If x = 27, then x + 2 is 29.

If x = -29, then x + 2 is -27.

The answer is:

There are two pairs of integers

One pair is 27 and 29.

The other pair is -29 and -27.

2. Answer:

(x)2+(x+2)2=1570

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