Given that ABC is not equal to 0, the square of AX + BX + C = 0, the square of BX + CX + a = 0, the square of Cx + ax + B = 0, find its common root

Given that ABC is not equal to 0, the square of AX + BX + C = 0, the square of BX + CX + a = 0, the square of Cx + ax + B = 0, find its common root

Three formula addition (a + B + C) x & # 178; + (a + B + C) x + (a + B + C) = 0
(a+b+c)(x²+x+1)=0
Because X & # 178; + X + 1 = (x + 1 / 4) &# 178; + 3 / 4 ≥ 3 / 4 > 0
So a + B + C = 0
So when x = 1, the condition is satisfied
The common solution is x = 1