SOLUTION: find three consectuitve intergers such that twice the product of the first and second exceeds the square of the third by 4

Question 66038This question is from textbook an incremental development
: find three consectuitve intergers such that twice the product of the first and second exceeds the square of the third by 4 This question is from textbook an incremental development

Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
QUESTION:
find three consectuitve intergers such that twice the product of the first and second exceeds the square of the third by 4

ANSWER:

Here we have three consecutive numbers.....
So we can take three consecutive numbers as (x-1), x , (x+1)
Product of first and second is (x-1)*x = x^2 - x
Twice the Product of first and second is = 2(x^2 - x )

==> = 2x^2 - 2x

Now square of the third is = (x+1)^2

==> x^2 + 2x + 1

according to the question,... twice the product of the first and second exceeds the square of the third by 4

which implies.....

2x^2 - 2x = x^2 + 2x + 1 + 4 ( exceeds 4 means + 4 )

==> 2x^2 - 2x = x^2 + 2x + 5

subtract x^2 from bioth sides of the expression...

==>2x^2 - 2x - x^2 = x^2 + 2x + 5 -x^2

==> x^2 - 2x = 2x + 5

Subtract 2x from both sides....

==> x^2 - 2x - 2x = 2x + 5 - 2x

==> x^2 - 4x = 5

Again subtract 5 from both sides....

==> x^2 - 4x - 5 = 5 - 5

==> x^2 - 4x - 5 = 0

Here we have quadratic equation...Solve this function to get the value of "x"

Here we use the following method ,....

GFind two numbers such that whose sum is -4 and whose product is -5

Such two numbers are -5 and +1

So we can write the above equation as ....

x^2 - 5x + 1x - 5 = 0 ( split the middle term only)

(x^2 - 5x ) + (1x - 5 )= 0

==> x ( x - 5 ) + 1( x - 5) = 0

==> ( x- 5)(x + 1 ) = 0

==> either ( x- 5)= 0 or (x + 1 ) =0

( x- 5)= 0 ==> x = 5 and

(x + 1 )= 0 ==> x = -1

So we have two values for x that is 5 and -1

If x = 5, then numbers are (5-1), 5, (5+1)

That is 4,5 and 6

If we take x = -1, then the numbers are (-1-1), -1, (-1+1)
That is -2, -1 and 0

Hope you understood...

Regards.

praseena.

RELATED QUESTIONS
Find three consecutive odd intergers such that the product of the first and the seconds... (answered by MathLover1)

Find three consecutive negative integers such that 3 times the product of the first and... (answered by stanbon)

Find three consecutive odd interrgers such that the product of the first and the second... (answered by stanbon)

Find three consecutive positive intergers such that the product of the first and second... (answered by htmentor)

Find three consecutive integers such that the sum of the squares of the second and third... (answered by edjones)

find three consecutive odd integers such that twice the sum of the first and third... (answered by scott8148,ewatrrr)

find three consecutive intergers such that the product of the second and third is... (answered by josmiceli,Alan3354)

Find three consecutive integers such as the product of the first and the third exceeds... (answered by ewatrrr)

ind three consecutive odd integers such that the product of the first and second exceeds... (answered by drk)