Question

X,y and z are three consecutive even numbers if y^2 - 2 = 2x + 5Z find x,y and z​

Answer 1

6, 8, 10

Explanation:

x y and z are three consecutive even numbers

it means that you can write y = x + 2

and z = y + 2 = x + 4

so

`y^2-2=2x+5z\\ <=> (x+2)^2-2=2x+5(x+4)\\<=>x^2+4x+4-2=2x+5x+20`

`<=> x^2+4x+2=7x+20\\<=>x^2+4x+2-7x-20=0\\<=>x^2-3x-18=0\\<=>(x+3)(x-6)=0<=>(x=-3\ or \ x=6)`

so the solutions are

x = 6

y = 8

x = 10

Answer 2

6, 8, 10

Explanation:

x, y, z

y=x+2, z= x+4

• y²- 2= 2x+5z
• (x+2)²- 2= 2x+ 5(x+4)
• x²+4x+4-2= 2x+5x+20
• x²-3x-18=0

Solving the quadratic equation we get:

• x=6, then y= 8, z= 10

• x= -3 discarded as odd number