Question

the product of two consecutive even numbers is 12768.what is the greater number

Answer 1

Let the two consecutive even numbers be x and x+2
ATQ-
x (x+2) = 12768
x^2 + 2x - 12768 = 0
x^2 + 114x -112x -12768 = 0
x (x + 114) - 112 ( x + 114) = 0
(x+114)(x-112) = 0
x= -114 or x=112

Therefore two consecutive even no.s are 112 and 114 and among them 114 is the greater no.
And among - 114 and -112 , -112 is the greater no.

Answer 2

let greater consecutive even no → x
let smaller consecutive even no → x-2

Acc. to the question

(x)(x-2)=12768

x^2-2x-12768=0

x = (-b ± √b^2-4ac)/2a
x = (2 ± √4-4.1.-12768)/2
x = (2 ± √51076)/2
x = (2 ± 226)/2
x = (2)(1 ± 113)/2
x = 1 ± 113

x = 1+113 | x = 1 - 113
x = 114, -112 ←←←←

Greater No. is 114.

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