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

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 Click here to see ALL problems on Numbers Word Problems 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 4This 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.