Question

Question 13
The product of two consecutive even numbers is 8 more than quadruple their sum. Find the numbers​

Answer 1

Step-by-step explanation:

Let the numbers be x and x+2

Given, x(x+2)−2(x+x+2)>20

=>x2+2x−2(2x+2)>20

=>x2+2x−4x−4>20

=>x2−2x−24>0

=>x2−6x+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