Question

find three consecutive integers whose sum and product are equal.

Please give a good answer... ​

Answer 1

ANSWER

Here, Let the three consecutive integers be x,x+1 and x-1.

Now, according to the question=>

x+(x+1)+(x-1) = x(x-1)(x+1)

=>3x = = x(x^2 -1)

=>3 = x^2 -1

=> x = -2 or 2.

Now, the threeconsecutive numbers will be either 1, 2,and 3 or (-1),( -2) and (-3).

Remember

1)When 3 numbers are in then=>

The terms are a,a-d and a+d.

2)When 4 terms are in Ap=>

The terms will be a-d,a-2d,a+2d and a+d.

3)But when we are told to take 3 consecutive terms then we can take=>

The terms as x,x+1 and x+3.

where x = the middle term.

For taking consecutive numbers till nth term=>

We have=>x+1,x+2,x+3,.........x+n

where x = the middle term.

and n= required no. of the term

where x+n is the last term.

Answer 2

Answer:

Let the three integers be x - 1 , x  and x + 1 .

Sum of the three integers = x - 1 + x + x + 1 .

Product of the integers = x ( x - 1 )( x + 1 ) .

The sum and product are equal .

So :

x ( x + 1 )( x - 1 ) = x - 1 + x + 1 + x

Use the formula of ( a + b )( a - b ) = a² - b²

⇒ x ( x² - 1 ) = 3 x

⇒ x² - 1 = 3

⇒ x² = 4

⇒ x = ±2

When x = 2 ,

Numbers are 1 , 2 , 3 .

When x = - 2 ,

Numbers are - 1 , - 2 , - 3 .

Hence these are the 2 possible solutions .

Step-by-step explanation:

Consecutive integers are defined as the numbers ( without any decimal or fraction ) that can be formed by adding 1 to the previous number .

It can include negative numbers too .

Now that we known what is a consecutive integer we should also know that when x² = a , then the value of x can + a or - a .

Hence we write x = ± a .