Answer:
6, 8 and 10 and -2, 0, 2
There are two roots x = -2 and 6,
but the since I don't believe 0 is an even number the answer is 6, 8 and 10
I was incorrect according to G0ggle zero is an even number so another answer is -2, 0, 2
Step-by-step explanation:
read the question and convert the English to mathematics
x, y and z even consecutive number
y = x+2
z = y+2 = x+4
and
xyz = x³ + y² + 2z² substitiute x terms in for y and z
x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solve for x by graphing on DEMOS
x = -2, 6 solved algebraically below
x = -2 y=0 z=2
x = 6 y=8 z=10
Checked both answers
xyz = x³ + y² + 2z²
-2(0)2 = -8 + 0 + 8 when x = -2
0 = 0
and
6(8)(10) = 6³ + 8² +2(10)² when x = 6
480 = 216+64+200
= 480
x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solved algebraically
(x²+2x)(x+4) = x³ + x² +4x +4 + 2x² + 16x + 32
x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32
x³ + 6x² + 8x = x³ + 3x² + 20x + 36
3x² - 12x - 36 = 0 factor out the 3
3[x² - 4x - 12] = 0
3(x+2)(x-6) = 0 x = -2 and -12
