Question

20．設(shè)集合A={1，1+d，1+2d}，B={1，q，q²}，若A=B，求d與q的值．

Answer 1

分析 由元素的互異性可知：d≠0，q≠±1，a≠0，而A=B可得$\left\{\begin{array}{l}{1+d=q}\\{1+2d={q}^{2}}\end{array}\right.$①或$\left\{\begin{array}{l}{1+d={q}^{2}}\\{1+2d=q}\end{array}\right.$②．解出方程組即可．

解答 解：由元素的互異性可知：d≠0，q≠±1，a≠0，而A=B．
∴$\left\{\begin{array}{l}{1+d=q}\\{1+2d={q}^{2}}\end{array}\right.$①或$\left\{\begin{array}{l}{1+d={q}^{2}}\\{1+2d=q}\end{array}\right.$②．．
由方程組①解得$\left\{\begin{array}{l}{d=0}\\{q=1}\end{array}\right.$，應(yīng)舍去；
由方程組②解得$\left\{\begin{array}{l}{d=0}\\{q=1}\end{array}\right.$（應(yīng)舍去）或$\left\{\begin{array}{l}{d=-\frac{3}{4}}\\{q=-\frac{1}{2}}\end{array}\right.$．
綜上可知：d=-$\frac{3}{4}$，q=-$\frac{1}{2}$．

點(diǎn)評(píng) 本題考查了集合元素的互異性、集合相等，屬于基礎(chǔ)題．