已知a^2+b^2-2（a+2b）=-5,求方程abx^2+bx+ax+a=0的解

Question

已知a^2+b^2-2（a+2b）=-5,求方程abx^2+bx+ax+a=0的解

Answer 1

(a^2 - 2a + 1) + (b^2 - 4b + 4) = 0;
(a-1)^2 + (b - 2)^2 = 0;
a = 1;
b = 2;
所以 abx^2+bx + ax +a = 0,即为：
2x^2 + 2x + x + 1 = 0;
2x^2 + 3x + 1 = 0;
(x+1)(2x + 1) = 0;
x1 = -1;
x2 = -1/2;