Question

The product of two consecutive even integers is 2 less than 5 times the smaller one.
What are the numbers?

Answer 1

Answer:

x=2 or x=1 where x is integer.

Step-by-step explanation:

even numbers are the multiple of 2 or which are perfectly divided by 2 i.e. 2,4,6 etc.

Let 'x' be the first even number and 'x+2' be the second even number.

now translate the given sentence into mathematical order we write as.

x*(x+2)=5x-2

now simplify for x we get the integer.

x*x+2x=5x-2

$x^{2}$=5x-2x-2

$x^{2}$=3x-2

$x^{2}$-3x+2=0

since above eqn is quadratic i.e. having greater power is 2, so using quadratic formula or middle term braking or completing square we get the value of x or integer.

using middle term braking we get the values of integers.

$x^{2}$-2x-1x+2=0

x(x-2)-1(x-2)=0

(x-2)(x-1)=0

x-2=0 and x-1=0

x=2 or x=1

verification

2*4=10-2

8=8