Two consecutive integers have a product of 132.Find the integers

1 answer:

7 0

The difference between consecutive integers is 1.
Let x = smaller integer.
Then x + 1 is the next greater consecutive integer.

x(x + 1) = 132

x^2 + x - 132 = 0

(x + 12)(x - 11) = 0

x + 12 = 0 or x + 11 = 0

x = -12 or x = -11

Since x is the smaller of the two integers, the answers are:
-12, -11
11, 12
There are two pairs of such integers.

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Answer:

$\displaystyle d = 4\sqrt{5}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)

Algebra II

Distance Formula: $\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step-by-step explanation:

Step 1: Define

Point (-5, 6) → x₁ = -5, y₁ = 6

Point (3, 2) → x₂ = 3, y₂ = 2

Step 2: Find distance d

Simply plug in the 2 coordinates into the distance formula to find distance d

Substitute in points [Distance Formulas]: $\displaystyle d = \sqrt{(3+5)^2+(2-6)^2}$
[Distance] [√Radical] (Parenthesis) Add/Subtract: $\displaystyle d = \sqrt{(8)^2+(-4)^2}$
[Distance] [√Radical] Evaluate exponents: $\displaystyle d = \sqrt{64+16}$
[Distance] [√Radical] Add: $\displaystyle d = \sqrt{80}$
[Distance] [√Radical] Simplify: $\displaystyle d = 4\sqrt{5}$