Question

2. The product of three consecutive integers is equal to 6 times the sum of the three integers. If the smallest integer is x, which of the following equations represent the above situation? Option 1: 2x" + x -9= 0 Option 2: x" + 2x + 18 = 0 Option 3: x" + 2x – 18=0 Option 4: 2x" — x +9= 0 ​

Answer 1

Step-by-step explanation:

1: 2x" + x -9= 0 Option 2: x" + 2x + 18 = 0 Option 3: x" + 2x – 18=0 Option 4: 2x" — x +9= 0

Answer 2

x³ + 3x² - 16x + 18 = 0 represents the above situation.

Given:

The product of 3 consecutive numbers is = 6 times their sum

smallest integer = x

To Find:

the equation that represents the given condition

Solution:

The smallest integer is x. Thus, the 3 integers will be- x, x + 1, x + 2

the sum of these 3 numbers will be = x + x + 1 + x + 2

= 3x + 3

the product of the 3 numbers will be = x(x + 1)(x + 2)

= x(x² + 2x + x + 2)

= x(x² + 3x + 2)

= x³ + 3x² + 2x

Thus, we can form the following equation-

x³ + 3x² + 2x = 6(3x + 3)

x³ + 3x² + 2x = 18x + 18

x³ + 3x² + 2x - 18x + 18 = 0

x³ + 3x² - 16x + 18 = 0

Thus, x³ + 3x² - 16x + 18 = 0 represents the above situation.

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