Question

find two consecutive positive even numbers if difference of their square is 20​

Answer 1

Answer:

42

Step-by-step explanation:

let the two consecutive even numbers be 2x,2x+2

given that |2x^2–(2x+2)^2|=84

i.e,4(|x^2-(x+1)^2|)=84

i.e,|x^2-(x+1)^2|=21

x^2-(x^2+1+2x)=+or-21

case 1:If positive is taken then -1–2x=+21 which implies x=-11

case 2:If negative is taken then -1–2x=-21 which implies x=10

Case 1 does not arise because when the value of x is substituted in the difference the answer is negative but it should be positive so neglect case 1

And let us go for case 2 the two consecutive integers are 2(10),2(10)+2 which are 20,22

At the last the sum of the two consecutive even integers is 20+22=42