Respuesta :
If x is the first number, x+2 is the next consecutive even integer. The difference (subtraction) of their squares equals 20. Therefore:
(x+2)²-x²=20...expand this:
x²+4x+4-x²=20
x²+4x+4-x²=20
4x+4=20
4x=16
x=4. Therefore the next consecutive even integer is x+2=6.
To check: 6²-4² must equal 20
36-16=20 check!
(x+2)²-x²=20...expand this:
x²+4x+4-x²=20
x²+4x+4-x²=20
4x+4=20
4x=16
x=4. Therefore the next consecutive even integer is x+2=6.
To check: 6²-4² must equal 20
36-16=20 check!
The positive even numbers are 4 and 6.
Equation
State of quality between two expressions consisting of variable and/or number.
Given
The difference of the squares of two positive consecutive even integers is 20.
To find
The number will be
How do find the numbers?
The difference of the squares of two positive consecutive even integers is 20.
Let x be the even number and positive consecutive even is (x+2)
Then according to the condition
[tex]\begin{aligned} (x+2)^{2} -x^{2} &=20\\x^{2} +4x+4-x^{2} &= 20\\4x &= 20-4\\4x &= 16\\x &= \dfrac{16}{4}\\x &= 4\end{aligned}[/tex]
Then the positive even numbers are 4 and 6.
More about the equation link is given below.
https://brainly.com/question/2263981
