Given | a | = 1, | B | = 2, | C | = 3, and a > b > C, find the value of ABC

Given | a | = 1, | B | = 2, | C | = 3, and a > b > C, find the value of ABC

If ABC satisfies a + B + C = 0 and a ^ 2 + B ^ 2 + C ^ 2 = 4, then the value of a ^ 4 + B ^ 4 + C ^ 4 is

Let a + B + C = x = 0, AB + BC + Ca = y,
Then y = - 2 is known from 4 = a ^ 2 + B ^ 2 + C ^ 2 = x ^ 2-2y
a^4+b^4+c^4=(a^2+b^2+c^2)^2-2[(ab)^2+(bc)^2+(ac)^2]
=16-2(y^2-2x*abc)
=16-2y^2
=8

It is known that a, B and C are all positive integers. If the square of a plus the square of C is equal to 10, the square of C plus the square of B is equal to 13, the value of ABC can be obtained

a²+c²=10 c²+b²=13
a=1,c=3,b=2
abc=6