Question

The product of two consecutive even numbers exceeds twice their sum by more than 20. Find the range of values that the smaller(x) of the numbers can take

• A. $x>6$
• B. $x<-4$
• C. $x>0$
• D. Both (1) and (2)

Answer 1

The correct option is D Both (1) and (2)

Let the numbers be $x$ and $x+2$
Given, $x(x+2)-2(x+x+2)>20$
$=>x^2+2x-2(2x+2)>20$
$=>x^2+2x-4x-4>20$
$=>x^2-2x-24>0$
$=>x^2-6x+4x-24>0$
$=>x(x-6)+4(x-6)>0$
$=>(x+4)(x-6)>0$
Case 1:
When $x+4>0;x-6>0$
$=>x>-4;x>6$
So, $x>6$ is the solution of case 1
Case 2:
When $x+4<0;x-6<0$
$=>x<-4;x<6$
So, $x<-4$ is the solution of case 2
So combined solution is $x>6$ and $x<-4$